title: The Caretaker

abstract: The Caretaker is a drama in three acts by Harold Pinter. Although it was the sixth of his major works for stage and television, this psychological study of the confluence of power, allegiance, innocence, and corruption among two brothers and a tramp, became Pinter's first significant commercial success. It premiered at the Arts Theatre Club in London's West End on 27 April 1960 and transferred to the Duchess Theatre the following month, where it ran for 444 performances before departing London for Broadway. In 1963, a film version of the play based on Pinter's unpublished screenplay was directed by Clive Donner. The movie starred Alan Bates as Mick and Donald Pleasence as Davies in their original stage roles, while Robert Shaw replaced Peter Woodthorpe as Aston. First published by both Encore Publishing and Eyre Methuen in 1960, The Caretaker remains one of Pinter's most celebrated and oft-performed plays.

text:
# The Caretaker

***The Caretaker*** is a drama in three acts by Harold Pinter. Although it was the sixth of his major works for stage and television, this psychological study of the confluence of power, allegiance, innocence, and corruption among two brothers and a tramp, became Pinter's first significant commercial success. It premiered at the Arts Theatre Club in London's West End on 27 April 1960 and transferred to the Duchess Theatre the following month, where it ran for 444 performances before departing London for Broadway. In 1963, a film version of the play based on Pinter's unpublished screenplay was directed by Clive Donner. The movie starred Alan Bates as Mick and Donald Pleasence as Davies in their original stage roles, while Robert Shaw replaced Peter Woodthorpe as Aston. First published by both Encore Publishing and Eyre Methuen in 1960, *The Caretaker* remains one of Pinter's most celebrated and oft-performed plays.

## Plot summary

### Act I

*A night in winter*

\[Scene 1\]

Aston has invited Davies, a homeless man, into his flat after rescuing him from a bar fight (7–9). Davies comments on the flat and criticises the fact that it is cluttered and badly kept. Aston attempts to find a pair of shoes for Davies but Davies rejects all the offers. Once he turns down a pair that doesn't fit well enough and another that has the wrong colour laces. Early on, Davies reveals to Aston that his real name is not "Bernard Jenkins", his "assumed name", but really "Mac Davies" (19–20, 25). He claims that his papers validating this fact are in Sidcup and that he must and will return there to retrieve them just as soon as he has a good pair of shoes. Aston and Davies discuss where he will sleep and the problem of the "bucket" attached to the ceiling to catch dripping rain water from the leaky roof (20–21) and Davies "*gets into bed*" while "ASTON *sits, poking his \[electrical\] plug* (21).

\[Scene 2\] *The* LIGHTS FADE OUT. *Darkness*.

LIGHTS UP. *Morning*. (21) As Aston dresses for the day, Davies awakes with a start, and Aston informs Davies that he was kept up all night by Davies muttering in his sleep. Davies denies that he made any noise and blames the racket on the neighbours, revealing his fear of foreigners: "I tell you what, maybe it were them Blacks" (23). Aston informs Davies that he is going out, but invites him to stay if he likes, indicating that he trusts him (23–24), something unexpected by Davies; for, as soon as Aston does leave the room (27), Davies begins rummaging through Aston's "stuff" (27–28) but he is interrupted when Mick, Aston’s brother, unexpectedly arrives, "*moves upstage, silently*", "*slides across the room*" and then suddenly "*seizes* Davies' "*arm and forces it up his back*", in response to which "DAVIES *screams*", and they engage in a minutely choreographed struggle, which Mick wins (28–29), ending Act One with the "*Curtain*" line, "What's the game?" (29).

### Act II

\[Scene 1\] *A few seconds later*

Mick demands to know Davies' name, which the latter gives as "Jenkins" (30), interrogates him about how well he slept the night before (30), wonders whether or not Davies is actually "a foreigner"—to which Davies retorts that he "was" indeed (in Mick's phrase) "Born and bred in the British Isles" (33)—going on to accuse Davies of being "an old robber \[…\] an old skate" who is "stinking the place out" (35), and spinning a verbal web full of banking jargon designed to confuse Davies, while stating, hyperbolically, that his brother Aston is "a number one decorator" (36), either an outright lie or self-deceptive wishful thinking on his part. Just as Mick reaches the climactic line of his diatribe geared to put the old tramp off balance—"Who do you bank with?" (36), Aston enters with a "bag" ostensibly for Davies, and the brothers debate how to fix the leaking roof and Davies interrupts to inject the more practical question: "What do you do . . . when that bucket's full?" (37) and Aston simply says, "Empty it" (37). The three battle over the "bag" that Aston has brought Davies, one of the most comic and often-cited Beckettian routines in the play (38–39). After Mick leaves, and Davies recognises him to be "a real joker, that lad" (40), they discuss Mick's work in "the building trade" and Davies ultimately discloses that the bag they have fought over and that he was so determined to hold on to "ain't my bag" at all (41). Aston offers Davies the job of Caretaker, (42–43), leading to Davies' various assorted animadversions about the dangers that he faces for "going under an assumed name" and possibly being found out by anyone who might "ring the bell called Caretaker" (44).

\[Scene 2\]
> THE LIGHTS FADE TO BLACKOUT.
>
> THEN UP TO DIM LIGHT THROUGH THE WINDOW.
> *A door bangs*.
> *Sound of a key in the door of the room*.
>
> DAVIES *enters, closes the door, and tries the light switch, on, off, on, off.*

It appears to Davies that "the damn light's gone now", but, it becomes clear that Mick has sneaked back into the room in the dark and removed the bulb; he starts up "*the electrolux*" and scares Davies almost witless before claiming "I was just doing some spring cleaning" and returning the bulb to its socket (45). After a discussion with Davies about the place being his "responsibility" and his ambitions to fix it up, Mick also offers Davies the job of "caretaker" (46–50), but pushes his luck with Mick when he observes negative things about Aston, like the idea that he "doesn't like work" or is "a bit of a funny bloke" for "Not liking work" (Davies' camouflage of what he really is referring to), leading Mick to observe that Davies is "getting hypocritical" and "too glib" (50), and they turn to the absurd details of "a small financial agreement" relating to Davies' possibly doing "a bit of caretaking" or "looking after the place" for Mick (51), and then back to the inevitable call for "references" and the perpetually necessary trip to Sidcup to get Davies' identity "papers" (51–52).

\[Scene 3\] *Morning*

Davies wakes up and complains to Aston about how badly he slept. He blames various aspects of the flat's set up. Aston suggests adjustments but Davies proves to be callous and inflexible. Aston tells the story of how he was checked into a mental hospital and given electric shock therapy, but when he tried to escape from the hospital he was shocked while standing, leaving him with permanent brain damage; he ends by saying, "I've often thought of going back and trying to find the man who did that to me. But I want to do something first. I want to build that shed out in the garden" (54–57). Critics regard Aston's monologue, the longest of the play, as the "climax" of the plot. In dramaturgical terms, what follows is part of the plot's "falling action".

### Act III

\[Scene 1\] *Two weeks later \[… \]Afternoon*.

Davies and Mick discuss the flat. Mick relates "(*ruminatively*)" in great detail what he would do to redecorate it (60). When asked who "would live there", Mick's response "My brother and me" leads Davies to complain about Aston's inability to be social and just about every other aspect of Aston's behaviour (61–63). Though initially invited to be a "caretaker", first by Aston and then by Mick, he begins to ingratiate himself with Mick, who acts as if he were an unwitting accomplice in Davies' eventual conspiracy to take over and fix up the flat without Aston's involvement (64) an outright betrayal of the brother who actually took him in and attempted to find his "belongings"; but just then Aston enters and gives Davies yet another pair of shoes which he grudgingly accepts, speaking of "going down to Sidcup" in order "to get" his "papers" again (65–66).

\[Scene 2\]  *That night*

Davies brings up his plan when talking to Aston, whom he insults by throwing back in his face the details of his treatment in the mental institution (66–67), leading Aston, in a vast understatement, to respond: "I . . . I think it's about time you found somewhere else. I don't think we're hitting it off" (68). When finally threatened by Davies pointing a knife at him, Aston tells Davies to leave: "Get your stuff" (69). Davies, outraged, claims that Mick will take his side and kick Aston out instead and leaves in a fury, concluding (mistakenly): "Now I know who I can trust" (69).

\[Scene 3\] *Later*

Davies reenters with Mick explaining the fight that occurred earlier and complaining still more bitterly about Mick's brother, Aston (70–71). Eventually, Mick takes Aston's side, beginning with the observation "You get a bit out of your depth sometimes, don't you?" (71). Mick forces Davies to disclose that his "real name" is Davies and his "assumed name" is "Jenkins" and, after Davies calls Aston "nutty", Mick appears to take offence at what he terms Davies' "impertinent thing to say", concludes, "I'm compelled to pay you off for your caretaking work. Here's half a dollar", and stresses his need to turn back to his own "business" affairs (74). When Aston comes back into the apartment, the brothers face each other", "*They look at each other. Both are smiling, faintly*" (75). Using the excuse of having returned for his "pipe" (given to him earlier through the generosity of Aston), Davies turns to beg Aston to let him stay (75–77). But Aston rebuffs each of Davies' rationalisations of his past complaints (75–76). The play ends with a "*Long silence*" as Aston, who "*remains still, his back to him \[Davies\], at the window*, apparently unrelenting as he gazes at his garden and makes no response at all to Davies' futile plea, which is sprinkled with many dots ("*. . .*") of elliptical hesitations (77–78).

## Origins and contexts of the play

According to Pinter's biographer Michael Billington, the playwright frequently discussed details of *The Caretaker*'s origins in relation to images from his own life. Billington notes in his authorised biography that Pinter said he had written the play while he and his first wife Vivien Merchant were living in Chiswick:

> \[The flat was\] a very clean couple of rooms with a bath and kitchen. There was a chap who owned the house: a builder, in fact, like Mick who had his own van and whom I hardly ever saw. The only image of him was of this swift mover up and down the stairs and of his van going . . . Vroom . . . as he arrived and departed. His brother lived in the house. He was a handyman . . . he managed rather more successfully than Aston, but he was very introverted, very secretive, had been in a mental home some years before and had had some kind of electrical shock treatment . . . ECT, I think . . . Anyway, he did bring a tramp back one night. I call him a tramp, but he was just a homeless old man who stayed three or four weeks.

According to Billington, Pinter described Mick as the most purely invented character of the three. For the tramp, Davies, however, he felt a certain kinship, writing "\[The Pinters' life in Chiswick\] was a very threadbare existence . . . very . . . I was totally out of work. So I was very close to this old derelict's world, in a way."(*Harold Pinter* 114–17).

For earlier critics, like Martin Esslin, *The Caretaker* suggests aspects of the Theatre of the Absurd, described by Esslin in his eponymous book coining that term first published in 1961; according to Esslin, absurdist drama by writers such as Samuel Beckett, Eugène Ionesco, Jean Genet, and Edward Albee, and others was prominent in the late 1950s and early 1960s as a reaction to chaos witnessed in World War II and the state of the world after the war.

Billington observes that "The idea that \[Davies\] can affirm his identity and recover his papers by journeying to Sidcup is perhaps the greatest delusion of all, although one with its source in reality"; as "Pinter's old Hackney friend Morris Wernick recalls, 'It is undoubtedly true that Harold, with a writer's ear, picked up words and phrases from each of us. He also picked up locales. The Sidcup in *The Caretaker* comes from the fact that the Royal Artillery HQ was there when I was a National Serviceman and its almost mythical quality as the fount of all permission and record was a source.' To English ears," Billington continues, "Sidcup has faintly comic overtones of suburban respectability. For Davies it is a Kentish Eldorado: the place that can solve all the problems about his unresolved identity and uncertain past, present and future" (122).

About directing a production of *The Caretaker* at the Roundabout Theatre Company in 2003, David Jones observed:

> The trap with Harold's work, for performers and audiences, is to approach it too earnestly or portentously. I have always tried to interpret his plays with as much humour and humanity as possible. There is always mischief lurking in the darkest corners. The world of The Caretaker is a bleak one, its characters damaged and lonely. But they are all going to survive. And in their dance to that end they show a frenetic vitality and a wry sense of the ridiculous that balance heartache and laughter. Funny, but not too funny. As Pinter wrote, back in 1960 : "As far as I am concerned The Caretaker IS funny, up to a point. Beyond that point, it ceases to be funny, and it is because of that point that I wrote it."

Hickling writes in this review of a production directed by Mark Babych in March 2009:

> \[*The Caretaker*\] remains, however, a remorselessly accurate record of its time. At the center of the drama is the horrifically indiscriminate use of shock therapy, which left one of the characters with brain damage; Matthew Rixon's disturbingly docile Aston is a brilliant portrait of the horrors inflicted by a supposedly civilised state. The climax comes in the harrowing monologue in which he recalls the moment the electrodes were attached. The lights close down on his traumatised features as he speaks, leaving us uncomfortably alone with his thoughts.

Pinter's own comment on the source of three of his major plays is frequently quoted by critics:

> I went into a room and saw one person standing up and one person sitting down, and few weeks later I wrote *The Room*. I went into another room and saw two people sitting down, and a few years later I wrote *The Birthday Party*. I looked through a door into a third room and saw two people standing up and I wrote *The Caretaker*.

## Analysis of the characters

**Aston**

When he was younger he was given electric shock therapy that leaves him permanently brain damaged. His efforts to appease the ever-complaining Davies may be seen as an attempt to reach out to others. He desperately seeks a connection in the wrong place and with the wrong people. His main obstacle is his inability to communicate. He is misunderstood by his closest relative, his brother, and thus is completely isolated in his existence. His good-natured attitude makes him vulnerable to exploitation. His dialogue is sparse and often a direct response to something Mick or Davies has said. Aston has dreams of building a shed. The shed to him may represent all the things his life lacks: accomplishment and structure. The shed represents hope for the future.

**Davies**

Davies manufactures the story of his life, lying or sidestepping some details to avoid telling the whole truth about himself. A non-sequitur. He adjusts aspects of the story of his life according to the people he is trying to impress, influence, or manipulate. As Billington points out, "When Mick suggests that Davies might have been in the services — and even the colonies, Davies retorts: 'I was over there. I was one of the first over there.' He defines himself according to momentary imperatives and other people's suggestions" (122).

**Mick**

At times violent and ill-tempered, Mick is ambitious. He talks above Davies' ability to comprehend him. His increasing dissatisfaction with Davies leads to a rapprochement with his brother, Aston; though he appears to have distanced himself from Aston prior to the opening of the play, by the end, they exchange a few words and a faint smile. Early in the play, when he first encounters him, Mick attacks Davies, taking him for an intruder in his brother Aston's abode: an attic room of a run-down house which Mick looks after and in which he enables his brother to live. At first, he is aggressive toward Davies. Later, it may be that by suggesting that Davies could be "caretaker" of both his house and his brother, Mick is attempting to shift responsibility from himself onto Davies, who hardly seems a viable candidate for such tasks. The disparities between the loftiness of Mick's "dreams" and needs for immediate results and the mundane realities of Davies's neediness and shifty non-committal nature creates much of the absurdity of the play.

## Style

The language and plot of *The Caretaker* blends Realism with the Theatre of the Absurd. In the Theatre of the Absurd language is used in a manner that heightens the audience's awareness of the language itself, often through repetition and circumventing dialogue.

The play has often been compared to *Waiting for Godot*, by Samuel Beckett, and other absurdist plays because of its apparent lack of plot and action.

The fluidity of the characters is explained by Ronald Knowles as follows: "Language, character, and being are here aspects of each other made manifest in speech and silence. Character is no longer the clearly perceived entity underlying clarity of articulation the objectification of a social and moral entelechy but something amorphous and contingent (41).

## Language

One of the keys to understanding Pinter's language is not to rely on the words a character says but to look for the meaning behind the text. The Caretaker is filled with long rants and non-sequiturs, the language is either choppy dialogue full of interruptions or long speeches that are a vocalised train of thought. Although the text is presented in a casual way, there is always a message behind its simplicity. Pinter is often concerned with "communication itself, or rather the deliberate evasion of communication" (Knowles 43).

The play's staccato language and rhythms are musically balanced through strategically placed pauses. Pinter toys with silence, where it is used in the play and what emphasis it places on the words when they are at last spoken.

## Mode of drama: Tragicomedy

*The Caretaker* is a drama of mixed modes; both tragic and comic, it is a tragicomedy. Elements of comedy appear in the monologues of Davies and Mick, and the characters' interactions at times even approach farce. For instance, the first scene of Act Two, which critics have compared to the hat and shoe sequences in Beckett's *Waiting for Godot*, is particularly farcical:

> ASTON *offers the bag to* DAVIES.
>
> MICK *grabs it*.
> ASTON *takes it*.
> MICK *grabs it*.
> DAVIES *reaches for it*.
> ASTON *takes it*.
> MICK *reaches for it*.
> ASTON *gives it to* DAVIES.
>
> MICK *grabs it*. *Pause*. (39)

Davies' confusion, repetitions, and attempts to deceive both brothers and to play each one off against the other are also farcical. Davies has pretended to be someone else and using an assumed name, "Bernard Jenkins". But, in response to separate inquiries by Aston and Mick, it appears that Davies' real name is not really "Bernard Jenkins" but that it is "Mac Davies" (as Pinter designates him "Davies" throughout) and that he is actually Welsh and not English, a fact that he is attempting to conceal throughout the play and that motivates him to "get down to Sidcup", the past location of a British Army Records Office, to get his identity "papers" (13–16).

The elements of tragedy occur in Aston's climactic monologue about his shock treatments in "that place" and at the end of the play, though the ending is still somewhat ambiguous: at the very end, it appears that the brothers are turning Davies, an old homeless man, out of what may be his last chance for shelter, mainly because of his (and their) inabilities to adjust socially to one another, or their respective "anti-social" qualities.

## Interpretation

In his 1960 book review of *The Caretaker*, fellow English playwright John Arden writes: "Taken purely at its face value this play is a study of the unexpected strength of family ties against an intruder." As Arden states, family relationships are one of the main thematic concerns of the play.

Another prevalent theme is the characters' inability to communicate productively with one another. The play depends more on dialogue than on action; however, though there are fleeting moments in which each of them does seem to reach some understanding with the other, more often, they avoid communicating with one another as a result of their own psychological insecurities and self-concerns.

The theme of isolation appears to result from the characters' inability to communicate with one another, and the characters' own insularity seems to exacerbate their difficulty communicating with others.

As the characters also engage in deceiving one another and themselves, deception and self-deception are motifs, and certain deceptive phrases and self-deceptive strategies recur as refrains throughout the dialogue. Davies uses an assumed name and has convinced himself that he is really going to resolve his problems relating to his lack of identity papers, even though he appears too lazy to take any such responsibility for his own actions and blames his inaction on everyone but himself. Aston believes that his dream of building a shed will eventually reach fruition, despite his mental disability. Mick believes that his ambitions for a successful career outweigh his responsibility to care for his mentally damaged brother. In the end however all three men are deceiving themselves. Their lives may continue on beyond the end of the play just as they are at the beginning and throughout it. The deceit and isolation in the play lead to a world where time, place, identity, and language are ambiguous and fluid.

## Production history

### Premiere

On 27 April 1960, the first production of *The Caretaker* opened at the Arts Theatre, in London, prior to transferring to the West End's Duchess Theatre on 30 May 1960. It starred Donald Pleasence as Davies, Alan Bates as Mick, and Peter Woodthorpe as Aston. The productions received generally strong reviews.

### Other notable productions and major revivals

* 1961 – Lyceum Theatre, New York City, on 4 October 1961 by Roger L. Stevens, Frederick Brisson, and Gilbert Miller. Directed by Donald McWhinnie. Setting: Bert Currah, Sets Supervised and lighting: Paul Morrison, Production Supervisor: Fred Herbert, Stage Manager/Understudy: Joel Fabiani

Cast: Alan Bates (Mick), Donald Pleasence (Davies), and Robert Shaw (Aston). Cast: Heinz Rühmann (Davies), Gerd Baltus (Aston) and Michael Schwarzmaier (Mick) * 1976 – Virginia Museum Theater (VMT), directed by James Kirkland. Part of the mission of the Virginia Museum at the time was to disseminate the arts, including drama, widely to the people of Virginia. In this regard, it is noteworthy that this was the second Pinter play to be produced by VMT, showing the increasing popularity of his works. This production followed the company's statewide tour of *The Homecoming* two years previously.
* 1981 – Royal National Theatre. Directed by Kenneth Ives.

Cast: Jonathan Pryce, Kenneth Cranham, and Warren Mitchell Cast: Charlie Drake (Davies), Jonathan Hackett (Aston) and Tim McInnerny (Mick). Michael Angelis also played one of the two brothers. Cast: Miriam Karlin played Davies – the first time a woman performed the title role – with Mark Lewis Jones (Aston) and Gary Lilburn (Mick). Directed by Annie Castledine. Cast: Donald Pleasence, Peter Howitt and Colin Firth * 1993 – The Studio Theatre, Washington, D.C. (12 September – 24 October)

Cast: Emery Battis, Richard Thompson, John Tindle. * 2000 – Comedy Theatre, London, November 2000 – February 2001. Directed by Patrick Marber. Designer, Rob Howell; lighting, Hugh Vanstone; sound, Simon Baker (for Autograph Sound). Associate Director, Gari Jones

Cast: Michael Gambon (Davies), Rupert Graves (Mick), and Douglas Hodge (Aston) Cast: Patrick Stewart (Davies), Aidan Gillen (Mick), and Kyle MacLachlan (Aston). Cast Robert Mandan (Davies), Steve Spiro (Mick) and Jaxon Duff Gwillim (Aston). Cast Nigel Harman, David Bradley, and Con O'Neill. * 2006–2007 – "Le gardien". Théâtre de l'Oeuvre. Transferred to the Théâtre de Paris. Directed by Didier Long.

Cast: Robert Hirsch, Samuel Labarthe and Cyrille Thouvenin. * 2007 – The English Theatre of Hamburg. Directed by Clifford Dean.

Cast: Hayward Morse, Steven Lello, and Scott Smith. Cast: Stephen Cartmell, Steven Epp, and Kris L. Nelson. * 2009 – Everyman Theatre, Liverpool. Directed by Christopher Morahan.

Cast: Jonathan Pryce (Davies), Peter McDonald (Aston), Tom Brooke (Mick). * 2010 – London Classic Theatre (touring production). Directed by Michael Cabot.

Cast: Nicholas Gadd, Nicholas Gasson, and Richard Stemp. * 2011 – Writers' Theatre, Glencoe, Illinois. Directed by Ron OJ Parson.

Cast: Kareem Bandealy, Anish Jethmalani and Bill Norris. * Broadcast on BBC Radio 4, 2:30PM Sat, 27 November 2010, repeated 2:30PM Sat, 28 April 2012: Davies read by David Warner, Aston by Tony Bell and Mick by Daniel Mays, directed by Peter Kavanagh.
* 2016 – The Old Vic Theatre, London. Directed by Matthew Warchus.

Cast: Timothy Spall, Daniel Mays, and George MacKay. Cast: Patrice Naiambana, David Judge, Jonathan Livingstone.

## Film adaptation

## Works cited

Arden, John. Book review of *The Caretaker*, by Harold Pinter. *New Theatre Mag.* 1.4 (July 1960): 29–30.

Billington, Michael. *Harold Pinter*. 1996. London: Faber and Faber, 2007. ISBN 978-0-571-23476-9 (13). Updated 2nd ed. of *The Life and Work of Harold Pinter*. 1996. London: Faber and Faber, 1997. ISBN 0-571-17103-6 (10). Print.

Esslin, Martin. *The Theatre of the Absurd*. 1961. 3rd ed. New York: Vintage Books, 2004. ISBN 1-4000-7523-8 (10). ISBN 978-1-4000-7523-2 (13). Print.

Hickling, Alfred. "The Caretaker: Octagon, Bolton". *Guardian*. Guardian Media Group, 13 March 2009. Web. 28 May 2009. (Rev. of production directed by Mark Babych.)

Jones, David. "Travels with Harold". *Front & Center Online*. Roundabout Theatre Company, Fall 2003. Web. 12 March 2009. ("Online version of the Roundabout Theatre Company's subscriber magazine.")

Knowles, Roland. The Birthday Party *and* The Caretaker*: Text and Performance*. London: Macmillan Education, 1988. 41–43. Print.

Naismith, Bill. *Harold Pinter*. Faber Critical Guides. London: Faber and Faber, 2000. ISBN 0-571-19781-7. Print.

Pinter, Harold. *The Caretaker: A Play in Three Acts*. London: Encore Publishing Co., 1960. OCLC 10322991. Print.

–––. The Caretaker *and* The Dumb Waiter*: Two Plays by Harold Pinter* 1960. New York: Grove Press, 1988. ISBN 0-8021-5087-X (10). ISBN 978-0-8021-5087-5 (13). Print.

Powlick, Leonard. " 'What the hell is that all about?' A Peek at Pinter's Dramaturgy." *Harold Pinter: Critical Approaches*. Ed. Steven H. Gale. Cranbury, NJ: Associated UP, 1986. 30–37. Print.

Richardson, Brian. Performance review of *The Caretaker*, Studio Theatre (Washington D.C.), 12 September 1993. *The Pinter Review: Annual Essays 1994*. Ed. Francis Gillen and Steven H. Gale. Tampa: U of Tampa P, 1994. 109–10. Print.

Scott, Michael, ed. *Harold Pinter:* The Birthday Party, The Caretaker, The Homecoming*: A Case Book*. London: Macmillan Education, 1986. Print.

## InfoBox

| The Caretaker | |
| --- | --- |
| First edition cover of *The Caretaker*, 1960 | |
| Written by | Harold Pinter |
| Characters | * Mick, *a man in his late twenties* * Aston, *a man in his early thirties* * Davies, *an old man* |
| Date premiered | 27 April 1960 |
| Place premiered | Arts Theatre<br>Westminster, London |
| Original language | English |
| Setting | A house in West London. Winter. |


title: Maltese nobility

abstract: The feudal system was first established in Malta by the Kingdom of Sicily, which conquered the island between 1090 and 1091. The Sicilian titles were abolished after the Arab occupation of Malta. From 1530 to 1798 the island was ruled by the Knights Hospitaller, and from 1800 to 1964 by the British. The Knights and the British both undertook to maintain the rights and privileges of the Maltese. In the later nineteenth century the British government gave official recognition to several noble titles that had been created by the Grand Masters of the Knights of Malta and other fontes honorum. There were 29 title holders: nine marquises, ten counts and ten barons. The nobles were styled "The Most Noble" and took precedence among themselves according to the date of creation of their titles. Some nobles were also styled as "Illustrissimo", which was however, disputed by Grand Master Vilhena. In the Italian fashion, their heirs-apparent were styled marchesino, contino or baroncino, as appropriate. Malta became an independent state in 1964 and a republic in 1974. Official recognition of titles of nobility by the Government of Malta were abolished in 1975. Even today, there are still Maltese noble families who live in Malta.

text:
# Maltese nobility

The feudal system was first established in Malta by the Kingdom of Sicily, which conquered the island between 1090 and 1091. The Sicilian titles were abolished after the Arab occupation of Malta. From 1530 to 1798 the island was ruled by the Knights Hospitaller (who became known as the Knights of Malta), and from 1800 to 1964 by the British. The Knights and the British both undertook to maintain the rights and privileges of the Maltese.

In the later nineteenth century the British government gave official recognition to several noble titles that had been created by the Grand Masters of the Knights of Malta and other *fontes honorum*. There were 29 title holders: nine marquises, ten counts and ten barons. The nobles were styled "The Most Noble" and took precedence among themselves according to the date of creation of their titles. Some nobles were also styled as "Illustrissimo", which was however, disputed by Grand Master Vilhena. In the Italian fashion, their heirs-apparent were styled *marchesino*, *contino* or *baroncino*, as appropriate.

Malta became an independent state in 1964 and a republic in 1974. Official recognition of titles of nobility by the Government of Malta were abolished in 1975.

Even today, there are still Maltese noble families who live in Malta.


title: Football Manager of the Year (Germany)

abstract: The title Football Manager of the Year has been awarded in Germany since 2002. The award is determined by a poll of German football journalists from the Association of German Sports Journalists and the publication kicker. Eligible are German managers and non-German managers coaching in Germany.

text:
# Football Manager of the Year (Germany)

The title **Football Manager of the Year** (*Trainer des Jahres*) has been awarded in Germany since 2002. The award is determined by a poll of German football journalists from the Association of German Sports Journalists (*Verband der Deutschen Sportjournalisten*) and the publication kicker.

Eligible are German managers and non-German managers coaching in Germany.

## Football Managers of the Year

Felix Magath and Jürgen Klopp share the record for most award wins, with three each.

| Year | Manager | Team |
| --- | --- | --- |
| 2002 | Klaus Toppmöller | Bayer Leverkusen |
| 2003 | Felix Magath | VfB Stuttgart |
| 2004 | Thomas Schaaf | Werder Bremen |
| 2005 | Felix Magath | Bayern Munich |
| 2006 | Jürgen Klinsmann | Germany |
| 2007 | Armin Veh | VfB Stuttgart |
| 2008 | Ottmar Hitzfeld | Bayern Munich |
| 2009 | Felix Magath | VfL Wolfsburg |
| 2010 | Louis van Gaal | Bayern Munich |
| 2011 | Jürgen Klopp | Borussia Dortmund |
| 2012 | Jürgen Klopp | Borussia Dortmund |
| 2013 | Jupp Heynckes | Bayern Munich |
| 2014 | Joachim Löw | Germany |
| 2015 | Dieter Hecking | VfL Wolfsburg |
| 2016 | Dirk Schuster | Darmstadt 98 |
| 2017 | Julian Nagelsmann | TSG Hoffenheim |
| 2018 | Jupp Heynckes | Bayern Munich |
| 2019 | Jürgen Klopp | Liverpool |
| 2020 | Hansi Flick | Bayern Munich |
| 2021 | Thomas Tuchel | Chelsea |
| 2022 | Christian Streich | SC Freiburg |
| 2023 | Urs Fischer | Union Berlin |
| 2024 | Xabi Alonso | Bayer 04 Leverkusen |


title: Fabio Lopez

abstract: Fabio Lopez is an Italian football manager of Spanish descent and a former footballer. Lopez has coached many Italian academy clubs, scouted for Atalanta B.C. and ACF Fiorentina, and managed a number of clubs throughout Eastern Europe and Asia. He holds a UEFA Pro Coaching Licence. Lopez's first senior managerial role was at FK Banga Gargždai, starting in January 2007. He is known for his strong leadership qualities, his ability to analyse and solve problems and his excellent interpersonal and communication skills with players. He has been the head coach of Vietnamese club Thanh Hóa since 22 November 2019 and was sacked on 7 June 2020

text:
# Fabio Lopez

**Fabio Lopez** (born 17 June 1973) is an Italian football manager of Spanish descent and a former footballer. Lopez has coached many Italian academy clubs, scouted for Atalanta B.C. and ACF Fiorentina, and managed a number of clubs throughout Eastern Europe and Asia. He holds a UEFA Pro Coaching Licence.

Lopez's first senior managerial role was at FK Banga Gargždai, starting in January 2007. He is known for his strong leadership qualities, his ability to analyse and solve problems and his excellent interpersonal and communication skills with players.

He has been the head coach of Vietnamese club Thanh Hóa since 22 November 2019 and was sacked on 7 June 2020

## Playing career

A goalkeeper, Lopez started his playing career in the academy of A.S. Roma. Ultimately, he was forced into early retirement as a result of a serious knee injury picked up while playing with Agiatese in the 1992–93 season.

## Early years

Lopez graduated secondary school with a diploma in Rome. After retiring as a footballer, he went on to become a football coach for a number of semi-professional club and youth teams. At age 28, he won a Youth Cup in an international tournament in Umbria, coaching Roma's affiliate academy side. He obtained his UEFA Youth Coaching Licence in 2000.

## Coaching career

### Eurolimpia A.S. Roma Academy

In 1996, Lopez joined the youth coaching staff at Eurolimpia Roma (Affiliate Academy A.S. Roma) as a goalkeeper coach of the academy. In March 2007, Lopez obtained a UEFA A coaching licence (Italy second category licence), which made him eligible to work as head coach of many international leagues and clubs. Since then, he has completed further coaching qualifications, and now holds a UEFA Pro Licence.

### A.S. Roma Academy

In 2000, Lopez was hired by Roma's youth academy side. Roma won a provincial championship and three regional tournaments, with many members of the side going on to successful senior careers in Italy.

### FK Banga Gargždai

In the 2007–08 season, Lopez was approached by Lithuanian club FK Banga Gargždai as to take over as head coach (for the first time in his career). The season was very successful as the club reached cup the semi-finals and recorded the best defensive record in the league, conceding only 15 goals all season while suffering only 6 defeats. In 2008, he was an instructor of the UEFA B course for the Lithuanian Football Federation.

### FK Šiauliai

In the 2008–09 season, after success with FK Banga Gargždai, Lopez was hired by FC Siauliai. The club finished in fourth place in the league, in a season that included a record 11 consecutive games unbeaten.

### Sabah FA

In 2011, Lopez was approached by Sabah FA in Malaysia's Liga Premier competition to become their manager, however the club ultimately appointed him as technical director. After eight months, Lopez resigned from the role and moved to Indonesia where he coached Premier League club, PSMS Medan.

### PSMS Medan

In 2012, Lopez saved the team from relegation with two games in advance. The club occupied a lowly league position upon his arrival, however he was able to secure safety by changing the mentality of the team.

### B.G. Sports Club

Lopez was then hired by Maldivian Premier League side B.G. Sports Club. Like his previous club, PSMS Madan, B.G. were also in a poor league position at the time of Lopez's arrival, their first 4 games all ending in defeat. After a series of important positive results, the team reached third place by the end of the season, which was considered a great success.

### Bangladesh national team

On 11 September 2015 Lopez was hired by the Bangladesh national team, He was hired with a short 4-month contract only for the qualifying matches at the 2018 World Cup in Russia

### Al-Orouba SC

Lopez's next role was at Omani club Al-Orouba SC, however once again his time was cut short, this time due to 'a difference in philosophy between the manager and the board'.

### Al-Ahli under 23s

After a 6-month coaching hiatus, Lopez returned to the managerial world by taking up a position as under 23s coach for Al-Ahli. Lying in 6th position at the time of his takeover, the club has registered 9 consecutive wins since his arrival, reaching the record of 7 victories without ever suffering a goal, taking them up to 2nd on the ladder.

### Borneo FC

On 5 January 2018 Lopez was hired as the new coach of Indonesian Liga 1 club Borneo FC, replacing Dejan Antonic. On 23 April 2019, he terminated his contract binding him to his employer by mutual consent of both parties.

### Thanh Hóa Football Club

On 22 November 2019 Lopez was hired as the new coach of Vietnamese club Thanh Hóa. After got only one win and four loss in the first five-game, he was sacked on 7 June 2020.

## Scouting career

### Atalanta B.C.

In 2003, Lopez became a scout for Atalanta B.C, where he remained until 2005.

### ACF Fiorentina

In 2005, Lopez moved from Atalanta to become a scout for ACF Fiorentina.

## Managerial statistics

| Team | Nat. | From | To | P | W | D | L | GS | GA | %W |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Bangladesh |  | 10 September 2015 | 27 November 2015 | 3 | 0 | 0 | 3 | 0 | 11 | 000.00 |

| Team | Nat. | From | To | P | W | D | L | GS | GA | %W |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| FK Banga Gargždai |  | 10 January 2007 | 27 March 2008 | 40 | 16 | 15 | 9 | 60 | 25 | 040.00 |

| Team | Nat. | From | To | P | W | D | L | GS | GA | %W |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| B.G. Sports Club |  | 3 March 2013 | 20 November 2013 | 15 | 7 | 3 | 5 | 23 | 10 | 046.67 |

### Managerial honours

Regional Cup Championship -

Three Regional Cup –

3 Place A Lyga FK Siauliai Championship

3 Place B.G. Sports Club Championship

2 Place Al-Ahli Saudi FC

## Personal life

Lopez is fluent in three languages (English, Italian & Lithuanian).

## InfoBox

Fabio Lopez
| Personal information | | | |
| --- | --- | --- | --- |
| Date of birth | (1973-06-17) 17 June 1973 | | |
| Place of birth | Rome, Italy | | |
| Position(s) | Goalkeeper | | |
| Senior career\* | | | |
| Years | **Team** | **Apps** | **(Gls)** |
| 1991–1993 | Agiatese F.C. | 48 | (0) |
|  | Atalanta B.C. (scout) | | |
| 2005–2007 | ACF Fiorentina (scout) | | |
| 2007–2008 | FK Banga Gargždai | | |
| 2008–2009 | FK Šiauliai | | |
| 2010–2011 | Sabah FA | | |
| 2011–2012 | PSMS Medan | | |
| 2013–2014 | B.G. Sports Club | | |
| 2015–2016 | Bangladesh | | |
| 2016 | Al-Orouba SC | | |
| 2016–2017 | Al-Ahli Saudi FC | | |
| 2017–2018 | Al-Ahli Saudi FC | | |
| 2019 | Borneo FC | | |
| 2019-2020 | Thanh Hóa | | |
| \*Club domestic league appearances and goals | | | |


title: İslamlar, Elmalı

abstract: İslamlar is a neighbourhood in the municipality and district of Elmalı, Antalya Province, Turkey. Its population is 541 (2022).

text:
# İslamlar, Elmalı

**İslamlar** is a neighbourhood in the municipality and district of Elmalı, Antalya Province, Turkey. Its population is 541 (2022).

## InfoBox

| İslamlar | |
| --- | --- |
| Neighbourhood | |
| İslamlarLocation in Turkey | |
| Coordinates: 36°37′58″N 29°45′59″E / 36.6329°N 29.7663°E / 36.6329; 29.7663 | |
| Country | Turkey |
| Province | Antalya |
| District | Elmalı |
| Population (2022) | 541 |
| Time zone | UTC+3 (TRT) |


title: Football Mogul

abstract: Football Mogul is a series of sports-simulation games that allows a player to play the owner, head coach or general manager of a National Football League franchise. The most recent version is Football Mogul 21. The original Football Mogul was released on March 30, 1999, a year after the release of the first Baseball Mogul.

text:
# Football Mogul

***Football Mogul*** is a series of sports-simulation games that allows a player to play the owner, head coach or general manager of a National Football League (pro American football) franchise. The most recent version is *Football Mogul 21*.

The original *Football Mogul* was released on March 30, 1999, a year after the release of the first *Baseball Mogul*.

## Games

| Title | Year | Developer | Publisher | Ref |
| --- | --- | --- | --- | --- |
| *Football Mogul* | 1999 | Infinite Monkey Systems | WizardWorks |  |
| *Football Mogul 2003* | 2002 | Sports Mogul | Sports Mogul |  |
| *Football Mogul 2005* | 2004 | Sports Mogul | Sports Mogul |  |
| *Football Mogul 2006* | 2005 | Sports Mogul | Sports Mogul |  |
| *Football Mogul 2007* | 2006 | Sports Mogul | Enlight Software |  |
| *Football Mogul 2008* | 2007 | Sports Mogul | Sports Mogul |  |
| *Football Mogul 2009* | 2008 | Sports Mogul | Sports Mogul |  |
| *Football Mogul 2010* | 2009 | Sports Mogul | Sports Mogul |  |
| *Football Mogul 2011* | 2010 | Sports Mogul |  |  |
| *Football Mogul 2012* | 2011 | Sports Mogul |  |  |
| *Football Mogul 2013* | 2012 | Sports Mogul |  |  |
| *Football Mogul 2014* | 2013 | Sports Mogul |  |  |
| *Football Mogul 15* | 2014 | Sports Mogul |  |  |
| *Football Mogul 16* | 2015 | Sports Mogul |  |  |
| *Football Mogul 17* | 2016 | Sports Mogul |  |  |
| *Football Mogul 18* | 2017 | Sports Mogul |  |  |
| *Football Mogul 19* | 2018 | Sports Mogul |  |  |
| *Football Mogul 20* | 2019 | Sports Mogul |  |  |
| *Football Mogul 21* | 2020 | Sports Mogul |  |  |

## InfoBox

| Logo for the release of *Football Mogul 16*. | |
| --- | --- |
| Genre(s) | Sports simulation (American football) |
| Developer(s) | Sports Mogul (previously known as Infinite Monkey Systems) |
| Publisher(s) | Sports Mogul
**Previous:**
WizardWorks
Enlight Software |
| Platform(s) | Microsoft Windows |
| First release | *Football Mogul*
1999 |
| Latest release | *Football Mogul 21*
2020 |


title: Georgia Stevens

abstract: Georgia Ruth Stevens is a former English female rugby union player. She represented England at the 2006 Women's Rugby World Cup. She scored two tries in England's 69-7 win over Wales in the 2003 Women's Six Nations.

text:
# Georgia Stevens

**Georgia Ruth Stevens** (born 13 June 1973) is a former English female rugby union player. She represented England at the 2006 Women's Rugby World Cup. She scored two tries in England's 69-7 win over Wales in the 2003 Women's Six Nations.

## InfoBox

Georgia Stevens
| Birth name | Georgia Ruth Stevens |
| --- | --- |
| Date of birth | (1973-06-13) 13 June 1973 |
| Height | 1.71 m (5 ft 7+12 in) |
| Weight | 79 kg (174 lb; 12 st 6 lb) |
| Rugby union career | |
| **Position(s)**  Flanker  Senior career  **Years** **Team** **Apps** **(Points)**  Clifton   ()  International career  **Years** **Team** **Apps** **(Points)**  1998–????  England  71  (45) | |


title: François Blais (MNA)

abstract: François Blais is a Canadian politician from Quebec, who was elected to the National Assembly of Quebec in the 2014 election and named Minister of Employment. He represented the electoral district of Charlesbourg as a member of the Quebec Liberal Party. From February 27, 2015, to January 28, 2016, he served as Minister of Education, Recreation and Sports following the resignation of Yves Bolduc. After January 28, he returned to the Employment and Labour portfolio. He was defeated in the 2018 election by Jonatan Julien of the Coalition Avenir Québec. Prior to his election to the legislature, Blais was the dean of social sciences at Université Laval.

text:
# François Blais (MNA)

**François Blais** is a Canadian politician from Quebec, who was elected to the National Assembly of Quebec in the 2014 election and named Minister of Employment. He represented the electoral district of Charlesbourg as a member of the Quebec Liberal Party. From February 27, 2015, to January 28, 2016, he served as Minister of Education, Recreation and Sports following the resignation of Yves Bolduc. After January 28, he returned to the Employment and Labour portfolio.

He was defeated in the 2018 election by Jonatan Julien of the Coalition Avenir Québec.

Prior to his election to the legislature, Blais was the dean of social sciences at Université Laval.

## InfoBox

| François Blais | |
| --- | --- |
|  | |
|  | |
| Member of the National Assembly of Quebec for Charlesbourg | |
| **In office**<br>April 7, 2014  August 29, 2018 | |
| Preceded by | Denise Trudel |
| Succeeded by | Jonatan Julien |
|  | |
| Personal details | |
| Political party | Quebec Liberal Party |
| Profession | academic |
|  | |


title: Melaleuca cheelii

abstract: Melaleuca cheelii is a plant in the myrtle family, Myrtaceae and is endemic to the Wide Bay–Burnett region of Queensland. It is a shrub or tree to 10 m (33 ft) with white flowers and papery bark. It has been classified as "near threatened" by the government of Queensland.

text:
# Melaleuca cheelii

***Melaleuca cheelii*** is a plant in the myrtle family, Myrtaceae and is endemic to the Wide Bay–Burnett region of Queensland. It is a shrub or tree to 10 m (33 ft) with white flowers and papery bark. It has been classified as "near threatened" by the government of Queensland.

## Description

*Melaleuca cheelii* grows to a height of 8–10 m (26–33 ft). Its leaves are arranged in alternating opposite pairs (decussate), each leaf with an elliptic shape, 5–12.5 mm (0.2–0.5 in) long and 2–6 mm (0.08–0.2 in) wide.

The flowers are white to cream-coloured and arranged in spikes at the ends of the branches which continue to grow after flowering. The flower spikes are up to 40 mm (2 in) long and 20 mm (0.8 in) in diameter and carry 2 to 10 flowers. The petals are 2–2.7 mm (0.08–0.1 in) long and fall off after the flower has opened. The stamens are arranged in 5 bundles around the flower and each bundle has 8 to 18 stamens. The main flowering season is in September. After flowering, woody cup or barrel-shaped fruit develop in loose clusters, each fruit 4–4.5 mm (0.16–0.18 in) long.

## Taxonomy and naming

*Melaleuca cheelii* was first formally described in 1932 by Cyril Tenison White in *Proceedings of the Royal Society of Queensland* collected by White himself at "Traverston, mouth of the Burrum River, about 180 miles north of Brisbane, Queensland" noting that it was "common in wet places in sandy wallum country". The specific epithet (*cheelii*) honours Edwin Cheel (1872– 1951) who was a botanist at the state herbarium in Sydney.

## Distribution and habitat

This melaleuca occurs in wallum country near Bundaberg including in Burrum Coast National Park and the Meadowvale Nature Park in Bundaberg.

## Conservation status

This species has been classified as "near threatened" under the Government of Queensland *Nature Conservation (Wildlife) Amendment Regulation* (2010).

## Use in horticulture

Although not well known in cultivation, a specimen in the Australian National Botanic Gardens in Canberra is more than 20 years old. Others have grown successfully in Adelaide and Brisbane.

## InfoBox

| *Melaleuca cheelii* | |
| --- | --- |
|  | |
|
| Scientific classification | |
| Kingdom: | Plantae |
| *Clade*: | Tracheophytes |
| *Clade*: | Angiosperms |
| *Clade*: | Eudicots |
| *Clade*: | Rosids |
| Order: | Myrtales |
| Family: | Myrtaceae |
| Genus: | *Melaleuca* |
| Species: | ***M. cheelii*** |
| Binomial name | |
| ***Melaleuca cheelii***<br>C.T.White | |
|


title: Vasudevan Srinivas

abstract: Vasudevan Srinivas is an Indian mathematician working in algebraic geometry. He is a Distinguished Professor in the School of Mathematics Tata Institute of Fundamental Research, Mumbai. Srinivas is an elected Fellow of the Third World Academy of Sciences, American Mathematical Society, Indian National Science Academy, and the Indian Academy of Sciences. Srinivas received the BSc degree from Bangalore University and did his MS (1978) and PhD (1982) degrees at the University of Chicago. Spencer Bloch was his research supervisor. He began his academic career at the Tata Institute of Fundamental Research, Mumbai in 1983.

text:
# Vasudevan Srinivas

**Vasudevan Srinivas** (born 6 June 1958) is an Indian mathematician working in algebraic geometry. He is a Distinguished Professor in the School of Mathematics Tata Institute of Fundamental Research, Mumbai. Srinivas is an elected Fellow of the Third World Academy of Sciences, American Mathematical Society, Indian National Science Academy, and the Indian Academy of Sciences.

Srinivas received the BSc degree from Bangalore University and did his MS (1978) and PhD (1982) degrees at the University of Chicago. Spencer Bloch was his research supervisor. He began his academic career at the Tata Institute of Fundamental Research, Mumbai in 1983.

## Career

### Mathematical contributions

Srinivas works in the field of algebraic geometry; his particular subfields of interest include the areas of algebraic cycles, K-theory, commutative algebra and positive characteristic methods. He is well-known for the Bloch-Srinivas method of diagonal decomposition to study algebraic cycles. He has also made outstanding contributions to the study of algebraic cycles on singular varieties, an area of which he is essentially an originator. Among some of his other contributions are the resolution of the Zariski problem for linear systems (in collaboration with Steven Dale Cutkosky), the characterization of the projecive space among homogeneous spaces (in collaboration with Kapil Paranjape) and the characterization of rational singularities (in collaboration with Vikram Mehta).

Srinivas's book on "Algebraic K-theory" which grew out of his lectures on the topic at TIFR in 1986-87 is now a standard reference for the subject for beginning researchers in the area.

### Service

Srinivas has played an important role in the promotion of mathematics through various scientific bodies, in both advisory and administrative capacities. He served on the International Mathematical Union Executive Committee from 2011 to 2018. He serves on the editorial boards of several mathematics journals. He is presently the Chairman of the National Board for Higher Mathematics, India.

### Awards and distinctions

He was awarded the Shanti Swarup Bhatnagar Prize for Science and Technology in 2003, the highest science award in India, in the mathematical sciences category. In 2010, he was an invited speaker at the International Congress of Mathematicians held at Hyderabad.

#### Other awards/honours

* Indian National Science Academy Medal for Young Scientists, 1987
* B.M. Birla Science Prize in Mathematics for the year 1995
* Fellow of the Indian National Science Academy, New Delhi
* TWAS Prize (2008)
* Fellow of the American Mathematical Society, 2012
* Humboldt Research Award, 2013
* DFG Mercator Fellowship 2020-2024

## InfoBox

| Vasudevan Srinivas | |
| --- | --- |
| Srinivas in 2009 | |
| Born | 6 June 1958 |
| Nationality | Indian |
| Alma mater | Bangalore University<br>University of Chicago |
| Awards | Shanti Swarup Bhatnagar Prize (2003) |
| **Scientific career** | |
| Fields | Algebraic geometry in mathematics |
| Institutions | Tata Institute of Fundamental Research |
| Doctoral advisor | Spencer Janney Bloch |
| Doctoral students | Amalendu Krishna |
|  | |


title: Interpolation space

abstract: In the field of mathematical analysis, an interpolation space is a space which lies "in between" two other Banach spaces. The main applications are in Sobolev spaces, where spaces of functions that have a noninteger number of derivatives are interpolated from the spaces of functions with integer number of derivatives.

text:
# Interpolation space

In the field of mathematical analysis, an **interpolation space** is a space which lies "in between" two other Banach spaces. The main applications are in Sobolev spaces, where spaces of functions that have a noninteger number of derivatives are interpolated from the spaces of functions with integer number of derivatives.

## History

The theory of interpolation of vector spaces began by an observation of Józef Marcinkiewicz, later generalized and now known as the Riesz-Thorin theorem. In simple terms, if a linear function is continuous on a certain space *Lp* and also on a certain space *Lq*, then it is also continuous on the space *Lr*, for any intermediate r between p and q. In other words, *Lr* is a space which is intermediate between *Lp* and *Lq*.

In the development of Sobolev spaces, it became clear that the trace spaces were not any of the usual function spaces (with integer number of derivatives), and Jacques-Louis Lions discovered that indeed these trace spaces were constituted of functions that have a noninteger degree of differentiability.

Many methods were designed to generate such spaces of functions, including the Fourier transform, complex interpolation, real interpolation, as well as other tools (see e.g. fractional derivative).

## The setting of interpolation

A Banach space X is said to be *continuously embedded* in a Hausdorff topological vector space Z when X is a linear subspace of Z such that the inclusion map from X into Z is continuous. A **compatible couple** (*X*0, *X*1) of Banach spaces consists of two Banach spaces *X*0 and *X*1 that are continuously embedded in the same Hausdorff topological vector space Z. The embedding in a linear space Z allows to consider the two linear subspaces

$$X\_{0}\cap X\_{1}$$

and

$$X\_{0}+X\_{1}=\left\\{z\in Z:z=x\_{0}+x\_{1},\ x\_{0}\in X\_{0},\\,x\_{1}\in X\_{1}\right\\}.$$

Interpolation does not depend only upon the isomorphic (nor isometric) equivalence classes of *X*0 and *X*1. It depends in an essential way from the specific *relative position* that *X*0 and *X*1 occupy in a larger space Z.

One can define norms on *X*0*X*1 and *X*0 \+ *X*1 by

$$\\|x\\|\_{0}\cap X\_{1}:=\max \left(\left\\|x\right\\|\_{0},\left\\|x\right\\|\_{1}\right),$$

$$\\|x\\|\_{0}+X\_{1}:=\inf \left\\{\left\\|x\_{0}\right\\|\_{0}+\left\\|x\_{1}\right\\|\_{1}\ :\ x=x\_{0}+x\_{1},\\;x\_{0}\in X\_{0},\\;x\_{1}\in X\_{1}\right\\}.$$

Equipped with these norms, the intersection and the sum are Banach spaces. The following inclusions are all continuous:

$$X\_{0}\cap X\_{1}\subset X\_{0},\ X\_{1}\subset X\_{0}+X\_{1}.$$

Interpolation studies the family of spaces X that are **intermediate spaces** between *X*0 and *X*1 in the sense that

$$X\_{0}\cap X\_{1}\subset X\subset X\_{0}+X\_{1},$$

where the two inclusions maps are continuous.

An example of this situation is the pair (*L*1(**R**), *L*(**R**)), where the two Banach spaces are continuously embedded in the space Z of measurable functions on the real line, equipped with the topology of convergence in measure. In this situation, the spaces *Lp*(**R**), for 1 ≤ *p* ≤ ∞ are intermediate between *L*1(**R**) and *L*(**R**). More generally,

$$L^{p\_{0}(\mathbf {R} )\cap L^{p\_{1}(\mathbf {R} )\subset L^{p}(\mathbf {R} )\subset L^{p\_{0}(\mathbf {R} )+L^{p\_{1}(\mathbf {R} ),\ \ {\text{when}\ \ 1\leq p\_{0}\leq p\leq p\_{1}\leq \infty ,}}}}}$$

with continuous injections, so that, under the given condition, *Lp*(**R**) is intermediate between *L**p*0(**R**) and *L**p*1(**R**).

**Definition.** Given two compatible couples (*X*0, *X*1) and (*Y*0, *Y*1), an **interpolation pair** is a couple (*X*, *Y*) of Banach spaces with the two following properties: * The space *X* is intermediate between *X*0 and *X*1, and *Y* is intermediate between *Y*0 and *Y*1.
* If *L* is any linear operator from *X*0 \+ *X*1 to *Y*0 \+ *Y*1, which maps continuously *X*0 to *Y*0 and *X*1 to *Y*1, then it also maps continuously *X* to *Y*.

The interpolation pair (*X*, *Y*) is said to be of **exponent θ** (with 0 \< *θ* \< 1) if there exists a constant *C* such that

$$\\|L\\|\_{X,Y}\leq C\\|L\\|\_{0},Y\_{0}^{1-\theta }\\;\\|L\\|\_{1},Y\_{1}^{\theta }$$

for all operators L as above. The notation ||*L*||*X*,*Y* is for the norm of *L* as a map from *X* to *Y*. If *C* = 1, we say that (*X*, *Y*) is an **exact interpolation pair of exponent θ**.

## Complex interpolation

If the scalars are complex numbers, properties of complex analytic functions are used to define an interpolation space. Given a compatible couple (*X*0, *X*1) of Banach spaces, the linear space $\mathcal {F}(X\_{0},X\_{1})$ consists of all functions *f* : **C***X*0 \+ *X*1, that are analytic on *S* = {*z* : 0 \< Re(*z*) \< 1}, continuous on *S* = {*z* : 0 ≤ Re(*z*) ≤ 1}, and for which all the following subsets are bounded:

{*f*(*z*) : *z**S*} ⊂ *X*0 \+ *X*1, {*f*(*it*) : *t***R**} ⊂ *X*0, {*f*(1 + *it*) : *t***R**} ⊂ *X*1.

$\mathcal {F}(X\_{0},X\_{1})$ is a Banach space under the norm

$$\\|f\\|\_{{\mathcal {F}(X\_{0},X\_{1})}=\max \left\\{\sup \_{t\in \mathbf {R} }\\|f(it)\\|\_{0},\\;\sup \_{t\in \mathbf {R} }\\|f(1+it)\\|\_{1}\right\\}.}$$

**Definition.** For 0 \< *θ* \< 1, the **complex interpolation space** (*X*0, *X*1)*θ* is the linear subspace of *X*0 \+ *X*1 consisting of all values *f*(*θ*) when *f* varies in the preceding space of functions,

$$(X\_{0},X\_{1})\_{\theta }=\left\\{x\in X\_{0}+X\_{1}:x=f(\theta ),\\;f\in {\mathcal {F}(X\_{0},X\_{1})\right\\}.}$$

The norm on the complex interpolation space (*X*0, *X*1)*θ* is defined by

$$\ \\|x\\|\_{\theta }=\inf \left\\{\\|f\\|\_{{\mathcal {F}(X\_{0},X\_{1})}\ :\ f(\theta )=x,\\;f\in {\mathcal {F}(X\_{0},X\_{1})\right\\}.}}$$

Equipped with this norm, the complex interpolation space (*X*0, *X*1)*θ* is a Banach space.

**Theorem.** Given two compatible couples of Banach spaces (*X*0, *X*1) and (*Y*0, *Y*1), the pair ((*X*0, *X*1)*θ*, (*Y*0, *Y*1)*θ*) is an exact interpolation pair of exponent θ, i.e., if *T* : *X*0 \+ *X*1*Y*0 \+ *Y*1, is a linear operator bounded from *Xj* to *Yj*, *j* = 0, 1, then T is bounded from (*X*0, *X*1)*θ* to (*Y*0, *Y*1)*θ* and $\\|T\\|\_{\theta }\leq \\|T\\|\_{0}^{1-\theta }\\|T\\|\_{1}^{\theta }.$

The family of *Lp* spaces (consisting of complex valued functions) behaves well under complex interpolation. If (*R*, Σ, *μ*) is an arbitrary measure space, if 1 ≤ *p*0, *p*1 ≤ ∞ and 0 \< *θ* \< 1, then

$$\left(L^{p\_{0}(R,\Sigma ,\mu ),L^{p\_{1}(R,\Sigma ,\mu )\right)\_{\theta }=L^{p}(R,\Sigma ,\mu ),\qquad {\frac {1}{p}={\frac {1-\theta }{p\_{0}+{\frac {\theta }{p\_{1},}}}}}}}$$

with equality of norms. This fact is closely related to the Riesz–Thorin theorem.

## Real interpolation

There are two ways for introducing the **real interpolation method**. The first and most commonly used when actually identifying examples of interpolation spaces is the K-method. The second method, the J-method, gives the same interpolation spaces as the K-method when the parameter θ is in (0, 1). That the J- and K-methods agree is important for the study of duals of interpolation spaces: basically, the dual of an interpolation space constructed by the K-method appears to be a space constructed from the dual couple by the J-method; see below.

### K-method

The K-method of real interpolation can be used for Banach spaces over the field **R** of real numbers.

**Definition.** Let (*X*0, *X*1) be a compatible couple of Banach spaces. For *t* \> 0 and every *x**X*0 \+ *X*1, let

$$K(x,t;X\_{0},X\_{1})=\inf \left\\{\left\\|x\_{0}\right\\|\_{0}+t\left\\|x\_{1}\right\\|\_{1}\ :\ x=x\_{0}+x\_{1},\\;x\_{0}\in X\_{0},\\,x\_{1}\in X\_{1}\right\\}.$$

Changing the order of the two spaces results in:

$$K(x,t;X\_{0},X\_{1})=tK\left(x,t^{-1};X\_{1},X\_{0}\right).$$

Let

$$\begin{aligned}\\|x\\|\_{\theta ,q;K}&=\left(\int \_{0}^{\infty }\left(t^{-\theta }K(x,t;X\_{0},X\_{1})\right)^{q}\\,{\tfrac {dt}{t}\right)^{\frac {1}{q},&&0\<\theta \<1,1\leq q\<\infty ,\\\\|x\\|\_{\theta ,\infty ;K}&=\sup \_{t\>0}\\;t^{-\theta }K(x,t;X\_{0},X\_{1}),&&0\leq \theta \leq 1.\end{aligned}}}$$

The K-method of real interpolation consists in taking *K**θ*,*q*(*X*0, *X*1)  to be the linear subspace of *X*0 \+ *X*1 consisting of all x such that ||*x*||*θ*,*q*;*K* \< ∞.

#### Example

An important example is that of the couple (*L*1(**R**, Σ, *μ*), *L*(**R**, Σ, *μ*)), where the functional *K*(*t*, *f*; *L*1, *L*) can be computed explicitly. The measure μ is supposed σ-finite. In this context, the best way of cutting the function *f**L*1 \+ *L* as sum of two functions *f*0*L*1 and *f*1*L* is, for some *s* \> 0 to be chosen as function of t, to let *f*1(*x*) be given for all *x***R** by

$$f\_{1}(x)={\begin{cases}f(x)&|f(x)|\<s,\\\{\frac {sf(x)}{|f(x)|}&{\text{otherwise}\end{cases}}}}$$

The optimal choice of s leads to the formula

$$K\left(f,t;L^{1},L^{\infty }\right)=\int \_{0}^{t}f^{\*}(u)\\,du,$$

where *f*  is the decreasing rearrangement of *f*.

### J-method

As with the K-method, the J-method can be used for real Banach spaces.

**Definition.** Let (*X*0, *X*1) be a compatible couple of Banach spaces. For *t* \> 0 and for every vector *x**X*0*X*1, let $J(x,t;X\_{0},X\_{1})=\max \left(\\|x\\|\_{0},t\\|x\\|\_{1}\right).$

A vector x in *X*0 \+ *X*1 belongs to the interpolation space *J**θ*,*q*(*X*0, *X*1) if and only if it can be written as

$$x=\int \_{0}^{\infty }v(t)\\,{\frac {dt}{t},}$$

where *v*(*t*) is measurable with values in *X*0*X*1 and such that

$$\Phi (v)=\left(\int \_{0}^{\infty }\left(t^{-\theta }J(v(t),t;X\_{0},X\_{1})\right)^{q}\\,{\tfrac {dt}{t}\right)^{\frac {1}{q}\<\infty .}}$$

The norm of x in *J**θ*,*q*(*X*0, *X*1) is given by the formula

$$\\|x\\|\_{\theta ,q;J}:=\inf \_{v}\left\\{\Phi (v)\ :\ x=\int \_{0}^{\infty }v(t)\\,{\tfrac {dt}{t}\right\\}.}$$

### Relations between the interpolation methods

The two real interpolation methods are equivalent when 0 \< *θ* \< 1.

**Theorem.** Let (*X*0, *X*1) be a compatible couple of Banach spaces. If 0 \< *θ* \< 1 and 1 ≤ *q* ≤ ∞, then $J\_{\theta ,q}(X\_{0},X\_{1})=K\_{\theta ,q}(X\_{0},X\_{1}),$ with equivalence of norms.

The theorem covers degenerate cases that have not been excluded: for example if *X*0 and *X*1 form a direct sum, then the intersection and the J-spaces are the null space, and a simple computation shows that the K-spaces are also null.

When 0 \< *θ* \< 1, one can speak, up to an equivalent renorming, about *the* Banach space obtained by the real interpolation method with parameters θ and q. The notation for this real interpolation space is (*X*0, *X*1)*θ*,*q*. One has that

$$(X\_{0},X\_{1})\_{\theta ,q}=(X\_{1},X\_{0})\_{1-\theta ,q},\qquad 0\<\theta \<1,1\leq q\leq \infty .$$

For a given value of θ, the real interpolation spaces increase with q: if 0 \< *θ* \< 1 and  1 ≤ *q**r* ≤ ∞, the following continuous inclusion holds true:

$$(X\_{0},X\_{1})\_{\theta ,q}\subset (X\_{0},X\_{1})\_{\theta ,r}.$$

**Theorem.** Given 0 \< *θ* \< 1, 1 ≤ *q* ≤ ∞ and two compatible couples (*X*0, *X*1) and (*Y*0, *Y*1), the pair ((*X*0, *X*1)*θ*,*q*, (*Y*0, *Y*1)*θ*,*q*) is an exact interpolation pair of exponent θ.

A complex interpolation space is usually not isomorphic to one of the spaces given by the real interpolation method. However, there is a general relationship.

**Theorem.** Let (*X*0, *X*1) be a compatible couple of Banach spaces. If 0 \< *θ* \< 1, then $(X\_{0},X\_{1})\_{\theta ,1}\subset (X\_{0},X\_{1})\_{\theta }\subset (X\_{0},X\_{1})\_{\theta ,\infty }.$

#### Examples

When *X*0 = *C*(\[0, 1\]) and *X*1 = *C*1(\[0, 1\]), the space of continuously differentiable functions on \[0, 1\], the (*θ*, ∞) interpolation method, for 0 \< *θ* \< 1, gives the Hölder space *C*0,*θ* of exponent θ. This is because the K-functional *K*(*f*, *t*; *X*0, *X*1) of this couple is equivalent to

$$\sup \left\\{|f(u)|,\\,{\frac {|f(u)-f(v)|}{1+t^{-1}|u-v|}\ :\ u,v\in \[0,1\]\right\\}.}$$

Only values 0 \< *t* \< 1 are interesting here.

Real interpolation between *Lp* spaces gives the family of Lorentz spaces. Assuming 0 \< *θ* \< 1 and 1 ≤ *q* ≤ ∞, one has:

$$\left(L^{1}(\mathbf {R} ,\Sigma ,\mu ),L^{\infty }(\mathbf {R} ,\Sigma ,\mu )\right)\_{\theta ,q}=L^{p,q}(\mathbf {R} ,\Sigma ,\mu ),\qquad {\text{where }{\tfrac {1}{p}=1-\theta ,}}$$

with equivalent norms. This follows from an inequality of Hardy and from the value given above of the K-functional for this compatible couple. When *q* = *p*, the Lorentz space *L**p*,*p* is equal to *Lp*, up to renorming. When *q* = ∞, the Lorentz space *L**p*,∞ is equal to weak-*Lp*.

## The reiteration theorem

An intermediate space X of the compatible couple (*X*0, *X*1) is said to be of **class *θ*** if

$$(X\_{0},X\_{1})\_{\theta ,1}\subset X\subset (X\_{0},X\_{1})\_{\theta ,\infty },$$

with continuous injections. Beside all real interpolation spaces (*X*0, *X*1)*θ*,*q* with parameter θ and 1 ≤ *q* ≤ ∞, the complex interpolation space (*X*0, *X*1)*θ* is an intermediate space of class θ of the compatible couple (*X*0, *X*1).

The reiteration theorems says, in essence, that interpolating with a parameter θ behaves, in some way, like forming a convex combination *a* = (1 − *θ*)*x*0 \+ *θx*1: taking a further convex combination of two convex combinations gives another convex combination.

**Theorem.** Let *A*0, *A*1 be intermediate spaces of the compatible couple (*X*0, *X*1), of class *θ*0 and *θ*1 respectively, with 0 \< *θ*0*θ*1 \< 1. When 0 \< *θ* \< 1 and 1 ≤ *q* ≤ ∞, one has $(A\_{0},A\_{1})\_{\theta ,q}=(X\_{0},X\_{1})\_{\eta ,q},\qquad \eta =(1-\theta )\theta \_{0}+\theta \theta \_{1}.$

It is notable that when interpolating with the real method between *A*0 = (*X*0, *X*1)*θ*0,*q*0 and *A*1 = (*X*0, *X*1)*θ*1,*q*1, only the values of *θ*0 and *θ*1 matter. Also, *A*0 and *A*1 can be complex interpolation spaces between *X*0 and *X*1, with parameters *θ*0 and *θ*1 respectively.

There is also a reiteration theorem for the complex method.

**Theorem.** Let (*X*0, *X*1) be a compatible couple of complex Banach spaces, and assume that *X*0*X*1 is dense in *X*0 and in *X*1. Let *A*0 = (*X*0, *X*1)*θ*0 and *A*1 = (*X*0, *X*1)*θ*1, where 0 ≤ *θ*0*θ*1 ≤ 1. Assume further that *X*0*X*1 is dense in *A*0*A*1. Then, for every 0 ≤ *θ* ≤ 1, $\left(\left(X\_{0},X\_{1}\right)\_{0},\left(X\_{0},X\_{1}\right)\_{1}\right)\_{\theta }=(X\_{0},X\_{1})\_{\eta },\qquad \eta =(1-\theta )\theta \_{0}+\theta \theta \_{1}.$

The density condition is always satisfied when *X*0*X*1 or *X*1*X*0.

## Duality

Let (*X*0, *X*1) be a compatible couple, and assume that *X*0*X*1 is dense in *X*0 and in *X*1. In this case, the restriction map from the (continuous) dual $X'\_{j}$ of *Xj*, *j* = 0, 1, to the dual of *X*0*X*1 is one-to-one. It follows that the pair of duals $\left(X'\_{0},X'\_{1}\right)$ is a compatible couple continuously embedded in the dual (*X*0*X*1)′.

For the complex interpolation method, the following duality result holds:

**Theorem.** Let (*X*0, *X*1) be a compatible couple of complex Banach spaces, and assume that *X*0*X*1 is dense in *X*0 and in *X*1. If *X*0 and *X*1 are reflexive, then the dual of the complex interpolation space is obtained by interpolating the duals, $((X\_{0},X\_{1})\_{\theta })'=\left(X'\_{0},X'\_{1}\right)\_{\theta },\qquad 0\<\theta \<1.$

In general, the dual of the space (*X*0, *X*1)*θ* is equal to $\left(X'\_{0},X'\_{1}\right)^{\theta },$ a space defined by a variant of the complex method. The upper-θ and lower-θ methods do not coincide in general, but they do if at least one of *X*0, *X*1 is a reflexive space.

For the real interpolation method, the duality holds provided that the parameter *q* is finite:

**Theorem.** Let 0 \< *θ* \< 1, 1 ≤ *q* \< ∞ and (*X*0, *X*1) a compatible couple of real Banach spaces. Assume that *X*0*X*1 is dense in *X*0 and in *X*1. Then $\left(\left(X\_{0},X\_{1}\right)\_{\theta ,q}\right)'=\left(X'\_{0},X'\_{1}\right)\_{\theta ,q'},$ where $\tfrac {1}{q'}=1-{\tfrac {1}{q}.}$

## Discrete definitions

Since the function *t**K*(*x*, *t*) varies regularly (it is increasing, but 1/*t**K*(*x*, *t*) is decreasing), the definition of the *K**θ*,*q*-norm of a vector n, previously given by an integral, is equivalent to a definition given by a series. This series is obtained by breaking (0, ∞) into pieces (2*n*, 2*n*+1) of equal mass for the measure d*t*/*t*,

$$\\|x\\|\_{\theta ,q;K}\simeq \left(\sum \_{n\in \mathbf {Z} }\left(2^{-\theta n}K\left(x,2^{n};X\_{0},X\_{1}\right)\right)^{q}\right)^{\frac {1}{q}.}$$

In the special case where *X*0 is continuously embedded in *X*1, one can omit the part of the series with negative indices n. In this case, each of the functions *x**K*(*x*, 2*n*; *X*0, *X*1) defines an equivalent norm on *X*1.

The interpolation space (*X*0, *X*1)*θ*,*q* is a "diagonal subspace" of an *q*-sum of a sequence of Banach spaces (each one being isomorphic to *X*0 \+ *X*1). Therefore, when q is finite, the dual of (*X*0, *X*1)*θ*,*q* is a quotient of the *p*-sum of the duals, 1/*p* \+ 1/*q* = 1, which leads to the following formula for the discrete *J**θ*,*p*-norm of a functional *x'* in the dual of (*X*0, *X*1)*θ*,*q*:

$$\\|x'\\|\_{\theta ,p;J}\simeq \inf \left\\{\left(\sum \_{n\in \mathbf {Z} }\left(2^{\theta n}\max \left(\left\\|x'\_{n}\right\\|\_{0},2^{-n}\left\\|x'\_{n}\right\\|\_{1}\right)\right)^{p}\right)^{\frac {1}{p}\ :\ x'=\sum \_{n\in \mathbf {Z} }x'\_{n}\right\\}.}$$

The usual formula for the discrete *J**θ*,*p*-norm is obtained by changing n to *n*.

The discrete definition makes several questions easier to study, among which the already mentioned identification of the dual. Other such questions are compactness or weak-compactness of linear operators. Lions and Peetre have proved that:

**Theorem.** If the linear operator T is compact from *X*0 to a Banach space Y and bounded from *X*1 to Y, then T is compact from (*X*0, *X*1)*θ*,*q* to Y when 0 \< *θ* \< 1, 1 ≤ *q* ≤ ∞.

Davis, Figiel, Johnson and Pełczyński have used interpolation in their proof of the following result:

**Theorem.** A bounded linear operator between two Banach spaces is weakly compact if and only if it factors through a reflexive space.

### A general interpolation method

The space *q* used for the discrete definition can be replaced by an arbitrary sequence space *Y* with unconditional basis, and the weights *an* = 2*θn*, *bn* = 2(1−*θ*)*n*, that are used for the *K**θ*,*q*-norm, can be replaced by general weights

$$a\_{n},b\_{n}\>0,\ \ \sum \_{n=1}^{\infty }\min(a\_{n},b\_{n})\<\infty .$$

The interpolation space *K*(*X*0, *X*1, *Y*, {*an*}, {*bn*}) consists of the vectors x in *X*0 \+ *X*1 such that

$$\\|x\\|\_{0},X\_{1})}=\sup \_{m\geq 1}\left\\|\sum \_{n=1}^{m}a\_{n}K\left(x,{\tfrac {b\_{n}{a\_{n};X\_{0},X\_{1}\right)\\,y\_{n}\right\\|\_{Y}\<\infty ,}}$$

where {*yn*} is the unconditional basis of Y. This abstract method can be used, for example, for the proof of the following result:

**Theorem.** A Banach space with unconditional basis is isomorphic to a complemented subspace of a space with symmetric basis.

## Interpolation of Sobolev and Besov spaces

Several interpolation results are available for Sobolev spaces and Besov spaces on **R***n*,

$$\begin{aligned}&H\_{p}^{s}&&s\in \mathbf {R} ,1\leq p\leq \infty \\\&B\_{p,q}^{s}&&s\in \mathbf {R} ,1\leq p,q\leq \infty \end{aligned}$$

These spaces are spaces of measurable functions on **R***n* when *s* ≥ 0, and of tempered distributions on **R***n* when *s* \< 0. For the rest of the section, the following setting and notation will be used:

$$\begin{aligned}0&\<\theta \<1,\\1&\leq p,p\_{0},p\_{1},q,q\_{0},q\_{1}\leq \infty ,\\s,&s\_{0},s\_{1}\in \mathbf {R} ,\\s\_{\theta }&=(1-\theta )s\_{0}+\theta s\_{1},\\\\[4pt\]{\frac {1}{p\_{\theta }&={\frac {1-\theta }{p\_{0}+{\frac {\theta }{p\_{1},\\\\[4pt\]{\frac {1}{q\_{\theta }&={\frac {1-\theta }{q\_{0}+{\frac {\theta }{q\_{1}.\end{aligned}}}}}}}}}}}}}$$

Complex interpolation works well on the class of Sobolev spaces $H\_{p}^{s}$ (the Bessel potential spaces) as well as Besov spaces:

$$\begin{aligned}\left(H\_{0}^{s\_{0},H\_{1}^{s\_{1}\right)\_{\theta }&=H\_{\theta }^{s\_{\theta },&&s\_{0}\neq s\_{1},1\<p\_{0},p\_{1}\<\infty .\\\left(B\_{0},q\_{0}^{s\_{0},B\_{1},q\_{1}^{s\_{1}\right)\_{\theta }&=B\_{\theta },q\_{\theta }^{s\_{\theta },&&s\_{0}\neq s\_{1}.\end{aligned}}}}}}}$$

Real interpolation between Sobolev spaces may give Besov spaces, except when *s*0 = *s*1,

$$\left(H\_{0}^{s},H\_{1}^{s}\right)\_{\theta }=H\_{\theta }^{s}.$$

When *s*0*s*1 but *p*0 = *p*1, real interpolation between Sobolev spaces gives a Besov space:

$$\left(H\_{p}^{s\_{0},H\_{p}^{s\_{1}\right)\_{\theta ,q}=B\_{p,q}^{s\_{\theta },\qquad s\_{0}\neq s\_{1}.}}}$$

Also,

$$\begin{aligned}\left(B\_{0}^{s\_{0},B\_{1}^{s\_{1}\right)\_{\theta ,q}&=B\_{p,q}^{s\_{\theta },&&s\_{0}\neq s\_{1}.\\\left(B\_{0}^{s},B\_{1}^{s}\right)\_{\theta ,q}&=B\_{\theta }^{s}.\\\left(B\_{0},q\_{0}^{s\_{0},B\_{1},q\_{1}^{s\_{1}\right)\_{\theta }&=B\_{\theta },q\_{\theta }^{s\_{\theta },&&s\_{0}\neq s\_{1},p\_{\theta }=q\_{\theta }.\end{aligned}}}}}}}$$


title: W. R. Cave

abstract: William Rendall Cave was a grain merchant and shipowner in the early days of South Australia. He was a son of Charles Cave of Stoke-sub-Hamdon, South Somerset, and Susannah who came to Adelaide in 1848 or 1849 and settled at Gumeracha. William found employment with John McKinlay at his cattle station at Lake Victoria, New South Wales. Next the Chambers brothers gave him a job at their northernmost cattle property, Beltana Station, and he remained there for several years, becoming an expert bushman. He broke in most of the horses used by John McDouall Stuart's 1861 expedition across the continent to Port Darwin. He and John Chambers shod all their horses, and Cave made duplicate sets of horseshoes, possibly at Chambers' Bobmoonie Station where the explorers made their final base before pushing into the unknown. Despite his peripheral association with the Stuart expedition, he was prominent in the many jubilees held between 1883 and 1914. Early on he went to Port Adelaide and took up stevedoring work for William Younghusband, loading the Solway with the first full cargo of wheat from South Australia for London, and the Thomas Brown for Acraman, Main, Lindsay, & Co. But after six months on the wharfs he secured a position as overseer of "Thursk", a cattle station near Overland Corner belonging to John White, where he was associated with Sir Jenkin Coles.

text:
# W. R. Cave

**William Rendall Cave** (17 June 1842 – 6 July 1916) was a grain merchant and shipowner in the early days of South Australia.

He was a son of Charles Cave (died 1851) of Stoke-sub-Hamdon, South Somerset, and Susannah (1800 – 19 December 1862) who came to Adelaide in 1848 or 1849 and settled at Gumeracha. William found employment with John McKinlay at his cattle station at Lake Victoria, New South Wales. Next the Chambers brothers gave him a job at their northernmost cattle property, Beltana Station, and he remained there for several years, becoming an expert bushman.

He broke in most of the horses used by John McDouall Stuart's 1861 expedition across the continent to Port Darwin. He and John Chambers shod all their horses, and Cave made duplicate sets of horseshoes, possibly at Chambers' Bobmoonie Station where the explorers made their final base before pushing into the unknown. Despite his peripheral association with the Stuart expedition, he was prominent in the many jubilees held between 1883 and 1914.

Early on he went to Port Adelaide and took up stevedoring work for William Younghusband, loading the *Solway* with the first full cargo of wheat from South Australia for London (perhaps in May 1862), and the *Thomas Brown* for Acraman, Main, Lindsay, & Co. But after six months on the wharfs he secured a position as overseer of "Thursk", a cattle station near Overland Corner belonging to John White, where he was associated with Sir Jenkin Coles.

## In business

After a year at "Thursk" he returned to the Port, working as a shipping and customs clerk with his brother-in-law, James Rawlings (1820 – 27 January 1896). From July 1867 they were trading as Rawlings & Cave, general shipping merchants.

In September 1873 Rawlings left the business, which continued to trade under that name until July 1874, but in October 1873 Cave founded W. R. Cave & Co., with offices at Port Adelaide and Grenfell Street, Adelaide. The business steadily expanded especially in the grain trade, with agencies throughout South Australia and branches in the other States. His partners were his son, John R. Cave, his nephew, Charles H. Warren and for a time Frederick Charles Howard. They became South Australian agents for Howard Smith and Co from ?? to 1893 and McIlwraith, McEacharn & Co. Around 1914 the city offices moved to Flinders Street. Rawlings went on to found the very successful shipping agents J. Rawlings & Son.

## Shipping

W. R. Cave & Co. owned or chartered a large number of undistinguished coasting vessels, and from 1889 to 1893 shared a wharf with the Howard Smith Company. Three vessels made the news: *Gwydir*, *Ellen*, and *Simplon*.

On 18 June 1901 the barge *Gwydir* sunk with the loss of three seamen while being towed, lightly loaded with wheat, from Port Pirie to Port Adelaide by the tug *Eleanor*. Both *Gwydir* and *Eleanor* belonged to W. R. Cave & Co., so William absented himself from the Board for its hearings. The Court of Enquiry found Captain William Tulloch of the *Eleanor* not guilty of neglect. Cave was criticised under parliamentary privilege, to which answered in the newspapers.

The *Ellen* (also known as the SS Ellen) was a coastal freighter and trawler, which was wrecked in Gulf St Vincent at Morgan's Beach near Cape Jervis South Australia on Saturday, 12 December 1908.

He imported the trawler *Simplon* from England in 1909 with the intention of starting a trawl fishing industry in South Australian waters. In 1914 he lent her to the South Australian government for the relief of people suffering the effects of the economic depression which was underway at the time.

## Other activities

During the Boer War he was, with Sir Jenkin Coles and N. W. Stirling (1853–1916), involved in the selection and purchase of South Australian horses for the Bushmen's Corps and 4th Contingent in 1900. and with William Robertson. for the Fifth Contingent of 1901.

He discovered several fossils on the banks of the Warburton River, which he presented to the Port Adelaide Museum.

He was appointed a governor of St Peter's College in 1888.

He was a warden of the Marine Board from 1896 to 1901.

He was for many years a director of various marine insurance companies: Commercial Marine Insurance Company Pty., South British Fire and Marine Insurance Company of New Zealand and Imperial Fire Insurance Company, including periods as chairman and vice chairman. (There is a family connection here – from 1848 to December 1850 his father, Charles Cave, was vice-chairman of the Adelaide branch of Imperial Fire Insurance Company.)

He was appointed South Australian Consul for Chile (or "Chili" as it was then spelled) from 1903 to 1916.

Cave was a major sponsor of Joshua Ives' appointment as the University of Adelaide's first lecturer in music in 1885. It is also possible that he was a composer, as sheet music by a composer called W. R. Cave was published early in the 20th century. The National Library of Australia identifies the composer as William Rendell Cave (spelling the middle name's second vowel as an "e" rather than "a") (Due to a typing error in this library entry, the reference to his death year is inconclusive (given as "191")). Counter-evidence is the report in *The Musical Times* of 1 January 1891 of the performance of Mendelssohn's "Hymn of Praise" at the People's Palace, conducted by one W. R. Cave, and in the same journal of 1 September 1894, a book *New Violin and Violoncello Music*, with pieces by Gilbert R. Betjemann, J. W. Ivimey, W. R. Cave, ..., ..., etc.

## Family

William had a brother and six sisters who migrated to South Australia:

* John D(arby) Cave (c. 1822 – 20 October 1899) who married Helen James ( –1887) of Gumeracha on 28 November 1853 and was a prominent citizen of Greenock then Burra.
* Lucy Cave ( –1912) married George Warren (c. 1822 – 25 February 1895) of Gawler on 4 April 1855. George was brother of John Warren MLC.

* Charles H(erbert) Warren (17 January 1856 – 6 November 1917) married Alice Maria Downer (1862–1960). He was a partner in W. R. Cave & Co. and for a time its head. A daughter, Constance Jean Warren (1891–1977), married Sir Lavington Bonython on 11 December 1912. His second wife, she was appointed OBE in recognition of her many public activities.
* Sarah Cave (c. 1829 – 13 February 1903) married James Rawlings (c. 1820 – 27 January 1896) on 31 May 1854 James was head of J. Rawlings & Son, shipping agents.
* Mary Cave (c. 1831 – 20 October 1894) married David Thomas ( – before 1855) in 1849. She married again, to John Beaton Terrell (c. 1829 – 12 January 1873) on 20 January 1855.
* Martha Cave (c. 1833 – 5 December 1908) married Joseph Howard (died c. 28 March 1893) on 30 October 1851. They lived at Glenelg then Gawler on 4 November 1851.

* Frederick Charles Howard (c. 1856 – 20 April 1919) was a partner in W. R. Cave & Co. and later director of a number of companies, notably chairman of directors of the Broken Hill South mine.
* Annie Cave ( – 5 August 1900) married John Beavis Randell (1829 – 24 March 1876), brother of Captain Randell.
* Susan Cave ( – 1 June 1911) married William Clark (c. 1832 – 5 June 1907) of Angaston on 19 November 1856.

He married Barbara Grierson (1849 – 12 December 1896), daughter of Captain Thomas Grierson, on 18 April 1867. They had a residence at Woodville, then Semaphore from around 1874 to 1890, then 191 Brougham Place, North Adelaide. From 1884 they also had a summer residence "Pomona" at Mt. Lofty.

* (Ellen) May Cave (4 May 1868 – 8 October 1938) married Charles William Brebner (c. 1862 – 12 February 1945) on 10 April 1897. The solicitor Charles Cave Brebner was their son.
* Lucy Grierson Cave (3 August 1869 – 1950) married cousin Frederic Charles Howard on 3 February 1891. She was the owner of "Frimley", a mansion on Belair Road, Lower Mitcham.

* (Charles) Roy Howard (1891 – 17 August 1935) married Patience Constance Joan Hawker (28 March 1900 – 9 August 1995) on 19 September 1928. She was co-founder of Stawell School.
* Thomas Grierson "Tom" Cave (11 September 1870 – January 1886). Tom and his friend Alfred Muecke (son of H. C. E. Muecke) were drowned while holidaying at Chowilla, the station of a friend William Robertson.
* Annie Alma Cave (11 January 1872 – 25 December 1941) never married.
* Emily Marie Cave (11 June 1873 – 1957) married horse racing identity Charles Loftus Moorhouse (1872–1963) on 14 December 1901. Their son Thomas Kilner "Tom" Moorhouse (1905–1971) was also well known in racing circles.
* Hugo Charles Cave (18 May 1875 – 12 May 1944) married Ada May Bowman (died 12 March 1944) on 10 October 1904, lived at "Waverley", South Terrace (sold to the Adelaide Legacy Club, later consultants' rooms associated with St. Andrews Hospital). Their daughter Mary Cave (6 October 1915 – ) was a prominent socialite.
* John Rendall Cave (1 April 1877 – 1957) John was jailed for a year on a charge of murder, for helping procure an abortion for Antonie Helvig "Tony" Klemich, who died on 26 March 1908 of peritonitis. Mrs Lundberg, in whose care the infection occurred, refused to testify and was not charged. A similar death in 1904 was not mentioned in court. He married Elsie May Bissett (died 10 April 1937), living at St Peters and had a son on 2 May 1923. He later came to the attention of the police for failing to maintain his family and for not complying with a maintenance order. Her death notice mentions her parents but not husband.
* Edmund Howard Cave (1888–1962) married Ada Georgina Clare (17 August 1888 – 1966) on 16 August 1911, lived at Stirling West.


title: WRC 4

abstract: WRC 4: The Official Game of the FIA World Rally Championship is a racing video game developed by Evolution Studios for the PlayStation 2. It is the fourth rallying game to be officially licensed by the FIA World Rally Championship and is based on the 2004 WRC season.

text:
# WRC 4

***WRC 4: The Official Game of the FIA World Rally Championship*** (also known as ***WRC 4*** and ***WRC 2004***) is a racing video game developed by Evolution Studios for the PlayStation 2. It is the fourth rallying game to be officially licensed by the FIA World Rally Championship and is based on the 2004 WRC season.

## Gameplay

In a quick race, the player will play a randomly selected stage with a randomly selected car and driver. During the race, the player will have to beat a time trial (although this is not needed to advance in the game). The time target will be based on the 1st place time ranking. If beaten, the best time will be the new target time to beat. The Championship mode lets the player play through the 2004 WRC season. The player must play through this mode based on the real life calendar, following the schedule for the 2004 WRC season. Championship mode ends when all 16 rallies are played, but the player can stop playing after any stage, because the game saves after each stage is finished. The player can play all six stages in a rally, but normally the player will have to buy the stage to play it in other modes.

The Pro Driver Challenge is a career mode where the player takes the role of a rookie who has to start from the weak Super 1600 class and must complete a series of tasks to enter the WRC class. In Super Special Challenge, the player will play against an AI generated opponent in all SSS course in the country's alphabetical order instead of the season's chronology. In a single rally, the player will play all six stages in a selected rally. The test track mode lets the player practice their driving skills or take part in rally tests akin to the license tests of the *Gran Turismo* series.

## Reception

The game received "generally favorable reviews" according to the review aggregation website Metacritic. In Japan, where the game was localized and published by Spike on 7 April 2005, *Famitsu* gave it a score of all four eights for a total of 32 out of 40.

## InfoBox

| WRC 4 | |
| --- | --- |
| PAL cover art | |
| Developer(s) | Evolution Studios |
| Publisher(s) |  |
| Series | *World Rally Championship* |
| Platform(s) | PlayStation 2 |
| Release | * EU: 22 October 2004 * JP: 7 April 2005 |
| Genre(s) | Racing |
| Mode(s) | Single-player |


title: Gynenomis sericealis

abstract: Gynenomis sericealis is a moth in the family Crambidae. It was described by Wileman and South in 1917. It is found in Taiwan.

text:
# Gynenomis sericealis

***Gynenomis sericealis*** is a moth in the family Crambidae. It was described by Wileman and South in 1917. It is found in Taiwan.

## InfoBox

| *Gynenomis sericealis* | |
| --- | --- |
|
| Scientific classification | |
| Domain: | Eukaryota |
| Kingdom: | Animalia |
| Phylum: | Arthropoda |
| Class: | Insecta |
| Order: | Lepidoptera |
| Family: | Crambidae |
| Genus: | *Gynenomis* |
| Species: | ***G. sericealis*** |
| Binomial name | |
| ***Gynenomis sericealis***<br>(Wileman & South, 1917) | |
|
| Synonyms | |
| * *Syllepte sericealis* Wileman & South, 1917 | |


title: WPHZ

abstract: WPHZ 102.5 Lite FM is an FM radio station broadcasting an adult contemporary music format. Licensed to Orleans, Indiana, United States. The station is currently owned by Mitchell Community Broadcast Company and includes news programming from Fox News Radio.

text:
# WPHZ

**WPHZ** 102.5 Lite FM is an FM radio station broadcasting an adult contemporary music format. Licensed to Orleans, Indiana, United States. The station is currently owned by Mitchell Community Broadcast Company and includes news programming from Fox News Radio.

## History

The station was assigned the call sign WOTS on 1988-10-20. On 1992-06-16, the station changed its call sign to WWEG, on 2004-04-01 to WNUF, on 2005-01-01 to WQRJ, and on 2007-01-01 to the current WPHZ.

On January 1, 2019, WPHZ changed their format from active rock (after a few weeks of Christmas music) to adult contemporary, branded as "Lite FM 102.5". Currently broadcasts Intelligence for Your Life: The John Tesh Radio Show in the mornings, and also the Delilah After Dark Adult contemporary Form at night. All of these are centered around the music they play.

## Former shows

* Insert Morning Show Title Here
* hardDriveXL
* Homespun Edge
* Racing Rocks
* Rockline

## InfoBox

WPHZ
|  | |
| --- | --- |
|  | |
| Broadcast area | Bedford, Indiana |
| Frequency | 102.5 MHz |
| Branding | *102.5 Lite FM* |
| Programming | |
| Format | Adult Contemporary |
| Affiliations | Fox News Radio |
| Ownership | |
| Owner | Ad-Venture Media/Mitchell Broadcasting |
| Sister stations | WQRK, WBIW |
| History | |
| First air date | 1988 (as WOTS) |
| Former call signs | WOTS (1988–1992)
WWEG (1992–2004)
WNUF (2004–2005)
WQRJ (2005–2007) |
| Technical information | |
| Licensing authority | FCC |
| Facility ID | 43248 |
| Class | A |
| ERP | 6,000 watts |
| HAAT | 86 meters (282 ft) |
| Transmitter coordinates | 38°38′16.00″N 86°27′11.00″W / 38.6377778°N 86.4530556°W / 38.6377778; -86.4530556 |
| Links | |
| Public license information |  |
| Webcast | Listen live |
| Website | 1025litefm.com |


title: WPIB

abstract: WPIB is a Christian adult contemporary formatted broadcast radio station licensed to Bluefield, West Virginia, serving the New River Valley. WPIB is owned and operated by Positive Alternative Radio, Inc.

text:
# WPIB

**WPIB** is a Christian adult contemporary formatted broadcast radio station licensed to Bluefield, West Virginia, serving the New River Valley. WPIB is owned and operated by Positive Alternative Radio, Inc.

37°15′25″N 81°10′41″W / 37.257°N 81.178°W / 37.257; -81.178

## InfoBox

WPIB
|  | |
| --- | --- |
| Broadcast area | New River Valley |
| Frequency | 91.1 MHz |
| Branding | *Spirit FM* |
| Programming | |
| Format | Christian adult contemporary |
| Ownership | |
| Owner | Positive Alternative Radio, Inc. |
| Sister stations | WAMN |
| History | |
| First air date | 1995 |
| Technical information | |
| Licensing authority | FCC |
| Class | C1 |
| ERP | 12,000 Watts |
| HAAT | 361 meters |
| Translator(s) | 106.9 W295AI (Marion) |
| Links | |
| Public license information |  |
| Webcast | WPIB Webstream |
| Website | WPIB Online |


title: NGC 7716

abstract: NGC 7716 is an intermediate spiral galaxy located in the constellation Pisces. Its speed relative to the cosmic microwave background is 2,201 ± 26 km/s, which corresponds to a Hubble distance of 32.5 ± 2.3 Mpc. NGC 7716 was discovered by British astronomer John Herschel in 1831. The luminosity class of NGC 7716 is II and it has a broad HI line. According to the SIMBAD database, NGC 7716 is a candidate galaxy for the active galaxy classification. To date, twelve non-redshift measurements give a distance of 32.442 ± 5.854 Mpc, which is within the Hubble distance values.

text:
# NGC 7716

**NGC 7716** is an intermediate spiral galaxy located in the constellation Pisces. Its speed relative to the cosmic microwave background is 2,201 ± 26 km/s, which corresponds to a Hubble distance of 32.5 ± 2.3 Mpc (∼106 million ly). NGC 7716 was discovered by British astronomer John Herschel in 1831.

The luminosity class of NGC 7716 is II and it has a broad HI line. According to the SIMBAD database, NGC 7716 is a candidate galaxy for the active galaxy classification.

To date, twelve non-redshift measurements give a distance of 32.442 ± 5.854 Mpc (∼106 million ly), which is within the Hubble distance values.

## NGC 7716 group

NGC 7716 is a member of a galaxy group of the same name. NGC 7716 group contains 5 members. The other galaxies in this group are NGC 7714, NGC 7715, UGC 12690 and UGC 12709.

1. "By Name | NASA/IPAC Extragalactic Database". *ned.ipac.caltech.edu*. Retrieved 2024-07-10.
2. "New General Catalog Objects: NGC 7700 - 7749". *cseligman.com*. Retrieved 2024-07-10.
3. "By Name | NASA/IPAC Extragalactic Database". *ned.ipac.caltech.edu*. Retrieved 2024-07-10.
4. "NGC\_7716". *simbad.u-strasbg.fr*. Retrieved 2024-07-10.
5. "NED Query Results for NGC 7716". *ned.ipac.caltech.edu*. Retrieved 2024-07-10.
6. Garcia, A. M. (1993-07-01). "General study of group membership. II. Determination of nearby groups". *Astronomy and Astrophysics Supplement Series*. **100**: 47–90. ISSN 0365-0138.

## InfoBox

| NGC 7716 | |
| --- | --- |
| NGC 77116, as seen by the Hubble Space Telescope | |
| Observation data (J2000 epoch) | |
| Constellation | Pisces |
| Right ascension | 23h 36m 30s |
| Declination | +00° 17’ 50” |
| Apparent magnitude (B) | 12.9 |
| Surface brightness | 22.75 mag/arcsec2 |
| Characteristics | |
| Type | SAb |
| Other designations | |
| PGC 71883, UGC 12702, MCG 0-60-19, CGCG 381-13, IRAS 23339+0001 | |


abstract: Naas was a constituency represented in the Irish House of Commons to 1801. The Parliament of Ireland merged with the Parliament of Great Britain to form the Parliament of the United Kingdom on 1 January 1801. Thereafter Naas was represented by the Members for Kildare.

text:
# Naas (Parliament of Ireland constituency)

**Naas** was a constituency represented in the Irish House of Commons to 1801. The Parliament of Ireland merged with the Parliament of Great Britain to form the Parliament of the United Kingdom on 1 January 1801. Thereafter Naas was represented by the Members for Kildare.

## Members of Parliament

* 1559–1560 John Sherlock and Henry Draycott
* 1585 James Sherlock and Walter Lewes
* 1613–1615 Christopher Sherlock and William Lattin
* 1634–1635 Christopher Sherlock and William Archbold
* 1639–1642 Christopher Sherlock (expelled for non-attendance) and Nicholas Sutton (expelled for rebellion)
* 1642–1649 Dr Dudley Loftus
* 1661–1662 George Carr and Sir John Hoey

### 1689–1801

| Election |  | First member | First party |  | Second member | Second party |
| --- | --- | --- | --- | --- | --- | --- |
| 1689 *Patriot Parliament* |  | Viscount Dungan |  |  | Charles White |  |
| 1692 |  | John Aylmer |  |  | Nicholas Jones |  |
| 1695 |  | Richard Nevill |  |  | James Barry |  |
| 1703 |  | Alexander Gradon |  |  | Francis Spring |  |
| 1711 | | | |  | James Barry |  |
| 1713 |  | Thomas Burgh |  |  | Theobald Bourke |  |
| 1727 | | | |  | John Bourke |  |
| 1731 | | | |  | Thomas Burgh |  |
| 1759 | | | |  | Richard Burgh |  |
| 1761 | | | |  | Maurice Keating |  |
| 1763 | | | |  | John Bourke |  |
| 1768 | | | |  | John Bourke |  |
| 1777 | | | |  | Thomas Allan |  |
| 1783 | | | |  | Hugh Carleton |  |
| 1787 | | | |  | Sir Richard Gorges-Meredyth, 1st Bt |  |
| 1790 | | | |  | John Bourke |  |
| 1791 | | | |  | James Bond |  |
| 1795 | | | |  | George Damer, Viscount Milton |  |
| January 1798 |  | Hon. Thomas Pelham |  |  | Hon. Francis Hely-Hutchinson |  |
| 1798 |  | John Macartney |  | | | |
| 1801 |  | *Constituency disenfranchised* | | | | |

### Notes

## InfoBox

| Naas | |
| --- | --- |
| Former borough constituency<br>for the Irish House of Commons | |
| County | County Kildare |
| Borough | Naas |
| () ( ())–1801 (1801) | |
| Seats | 2 |
| Replaced by | Disfranchised |


title: WIN (detergent)

abstract: WIN High Performance Sports Detergent is a brand of laundry detergent launched in the United States in 2006 and also sold in Canada. It is designed specifically to clean high performance sports clothing made from microfibers and is marketed towards elite-level athletes and fitness enthusiasts. It is the first officially licensed detergent of the U.S. Olympic Team.

text:
# WIN (detergent)

**WIN High Performance Sports Detergent** is a brand of laundry detergent launched in the United States in 2006 and also sold in Canada. It is designed specifically to clean high performance sports clothing made from microfibers and is marketed towards elite-level athletes and fitness enthusiasts. It is the first officially licensed detergent of the U.S. Olympic Team.

## Technology

WIN is a surfactant, and its properties are used in conjunction with WIN's oxygenated system, which is built using hydrogen peroxide bleach (H2O2). The oxidization converts soil and stains into a soluble form that can be washed away by WIN's surfactant system. Hydrogen peroxide also provides a more gentle bleaching action than chlorine bleaches.

Until WIN, peroxide bleach in a liquid detergent had not been marketed primarily to target sweat-caused bacteria in clothing. Oxy-based cleaning systems necessitate a lower pH, which makes them generally less effective on certain household stains like oil or food, and can be difficult to formulate due to stability issues created by a loss of available oxygen over periods of time. However, WIN's cleaning system was designed not to be a general use detergent formula, but rather, to address the needs of its sports enthusiast target market.

## Charity Initiatives

In July 2008, WIN teamed up with Olympic decathlete Bryan Clay to announce a new charity initiative called “Take Your Shirts Off to WIN.” The program asks fans to donate workout apparel to WIN, who will wash the clothing and send it to Giving is Winning, an organization that promotes sport activities for the youth in refugee camps throughout the world.

1. United States Olympic Committee Press Release announcing licensing agreement