In a site at the internet, there was an intriguing entry:
Gilbert Adair:
     * Alice Through the Needle's Eye [Macmillan, 1984] ISBN 0-333-37361-8
          [Picador, 1985] ISBN 0-330-29158-0
          [Dutton, 1988] ISBN 0-525-48375-6
          sequel to Lewis Carroll's Alice novels
     * Peter Pan and the Only Children [1987]
     * The Death of the Author [1992] parody of Vladimir Nabokov
     * The Postmodernist Always Rings Twice [1992]
     * A Void [1994] translation which never uses the letter "e" of the
          novel by Georges Perec, which also never uses the letter "e"

The association to Nabokov is confirmed by an Evening Standard critic, Anthony Quinton: "In a brilliantly exact imitaton of the style of Nabokov, Leo Sfaz recounts his life-and-death story. Once a pro-Nazi journalist in France, now an academic hero in somewhere very like Yale, he applies the fashionable technique of deconstruction (text means anything the reader wants it to mean, the author's intentions are nothing, text does not really have authors) to conceal or invert his own ignominius past. But some neat muder mystification is found a place in this dazzling satire of literary-critical pertension."
One reads David Lodge's appraisal of The Death of The Author -Gilbert Adair: "Brillant, worthy of Nabokov."—David Lodge
In other sites, no similar reference. There is an interview with Adair at the Zembla site ( nabokov on television  Interviewees: Gilbert Adair, Carroll Baker, Leslie Dick, Emma Forest, James B. Harris, A.M. Homes, Jeremy Irons, Eric Kahane, Adrian Lyne, Dmitri Nabokov,
Links to Paul de Man, Barthes and no Nabokov are at Lizzy’s Literary Life: Celebrating the pleasures of a 21st century bookworm
The Death of the Author – Gilbert Adair September 29, 2009 by lizzysiddal -
Also at The complete review's review: "Apart from his many other talents Gilbert Adair is an excellent stylist... The Death of the Author is an exceptionally fine little novella..."A review and a link to other reviews of The Death of the Author by Gilbert Adair.
Gilbert Adair, himself, denies any determining influence by Nabokov in reply to a critical piece at the London Review of Books: Vol. 20 No. 1 · 1 January 1998 Vol. 20 No. 2 · 22 January 1998 : "As I read Lorna Sage’s perceptive, if occasionally puzzling, review of my novel The Key of the Tower (LRB, 1 January) – as, in particular, I read her contention that ‘Adair the novelist has the doubtful distinction of being almost entirely inspired, permeated, by Nabokov’s example’ – something inside me went snap. Now, I realise that when a writer denies an alleged influence, just as when a politician denies a rumoured sexual liaison, the denial seems only to confirm the truth of the allegation; but over the years Nabokov has become something of an albatross about my neck and I wonder if I might set the record straight. Thus: my very real admiration for his work has remained well this side of idolatry; not one of his books (with the possible exception of Pale Fire) is what I would consider an outright masterpiece; as for Ada, it’s the sort of unsalvageable calamity which befalls at least once in their creative lives all but the greatest of writers, an ex-clusive group to which Nabokov most emphatically does not belong; the late, post-Ada confections are each more flabbily written and indolently plotted than the last; and the fabled Nabokovian bewitchment, the undeniable spell cast by his style, works most potently, for me at least, at the paragraph and even sentence level. Let me add that I’m not endeavouring to defend myself in extremis against a ‘mixed’ review. Sage seems familiar with my critical essays and may therefore have read one I wrote two years ago in the Sunday Times in which I not merely expressed distaste for the preening Olympian hauteur of Nabokov the public man but described Lolita, the novel to which I would appear to be most toadyingly in thrall, as ‘unbearable’./ As a shameless poacher of idiolects, I’ve never tried to conceal from even a casual reader’s view the referential mode of any of my books. But for the benefit of any subsequent reviewer, they are as follows: The Holy Innocents : Cocteau’s Le Grand Ecart, Les Enfants terribles and Thomas l’imposteur. ;Love and Death on Long Island : Mann’s Death in Venice.; The Death of the Author: Henry James’s stories of the literary life, as in The Death of (the Lion) the Author (of Beltraffio).; The Key of the Tower: Hitchcock (as more than one reviewer noted). As for the purely linguistic quality of the latter book, I would say that even if in the English language Nabokov is still probably the most juicily metaphoric of stylists, there exist other languages and some of us read them. The writers I happened to be reading at the time of writing my book were all French – Proust, Cocteau, Giraudoux and Paul Morand, all of them, too, superior (yes, yes, in my opinion) to Nabokov. Like my novels or hate them – but give me and Nabokov a break!" Gilbert Adair

Another review: Gilbert Adair: And Then There Was No One January 4th, 2009 Stewart 
Gilbert Adair, in the third of his Evadne Mount novels, changes tack and disposes with the cosy Christie model subverted successfully in The Act Of Roger Murgatroyd and less so in A Mysterious Affair Of Style, by opting to throw himself into the mix and tell the story of And Then There Was No One (2009) as a fictional memoir. Set in 2011, Adair has found himself at a literary festival in a Swiss town by the Reichenbach Falls, setting for Conan Doyle’s attempt at ridding himself of his popular detective character.//The influence of Sherlock Holmes plays as much a part in And Then There Was No One as that of Agatha Christie has for the triptych of Evadne Mount novels, and fans of Holmes may be interested to know that Adair reproduces, in full from his fictional new book of Sherlock Holmes stories, his take on The Giant Rat Of Sumatra, first mentioned in The Adventure Of The Sussex Vampire (cf The Casebook Of Sherlock Holmes) as “a story for which the world is not yet prepared”.//The reason for this change in the style of the novels comes late, but is worth mentioning, as Adair regularly talks about his novels, past, present, and in translation throughout.[...]
Adair begins by playing with the conventions of the murder mystery genre. Where the murder didn’t occur until late in A Mysterious Affair Of Style, the murder has long since been wrapped up here. The victim is Gustav Slavorigin,  a Booker Prize-winning author sent, after publishing a collection of incendiary anti-American essays, into hiding....//The prologue, seemingly extraneous to the mystery itself, fills in details that, to a first read, seem dry and dull, and in doing so recalls both the introduction to Eco’s The Name Of The Rose and the short foreword to Nabokov’s Lolita. This in itself is strange, given that Adair has mentioned in the past that Nabokov has “become something of an albatross about [his] neck”. The details of this chapter deal with the history of Slavorigin - his early days at university, with Adair, through the rise, fall, and infamy of his writing career. One notable book, and the reason Slavorigin is making a rare public pitstop, is his new thriller, A Reliable Narrator, which gives the game away without, if you catch my drift, doing so.//
"How to describe A Reliable Narrator? Its opening chapter resembles the concluding chapter of a whodunnit, one that just happens never actually to have been written. Thus the reader of Slavorigin’s book (I mean, the book which was written) cannot hope to comprehend the picturesque twists of this first-chapter denouement since, of the murder which has clearly taken place, the only detail to which he is made privy is the identity of the murderer, a murderer who has already been apprehended, charged, tried, found guilty and sentenced to life imprisonment."
The idea of a reliable narrator is played around with too, as is Adair’s playful style. Personal views come into the fray, such  as calling the forty-five minutes of literary festivals “so much hassle for so little result” and his description of a book as being “a fat, virtuosically executed novel by one of that new breed of American wunderkinder who, I would be lying if I denied it, are positively bloated with talent but who are also just too fucking pleased with themselves.” As a fictional Adair, he’s able to get away with it, even if, with reference to Slavorigin’s book:.// The first-person protagonist is no canonic unreliable narrator, such a tired old cliché of postmodernism now, but a perfectly reliable narrator, except that not a single soul is prepared to rely on him.//The usual alliteration, literary and cinematic in-jokes, and postmodern trickery are present and accounted for in And Then There Was No One. The unashamed use of puns (’Google Gogol’, a delicatessen named ‘Salvador Deli’ and a few more Nabokovian references, ‘Son of Palefire’ and ‘Adair or Ardor’) adds to the fun, and I’d like to think that only Adair’s style, like a British eccentric, could get away with a metaphor like “the train tranquilly unzipped the country’s flies from Oxford to London”.// Amongst the answers at that session there are some interesting insights that, if we believe the reliable narrator, into Adair that show And Then There Was No One as being that personal work...

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