John Banville's 'Frames' trilogy is centred around the charmingly unlikeable Freddie Montgomery. No, unlikeable is too strong - for, while he is not likeable in any conventional sense, it's hard not to be drawn to him. In 'The Book of Evidence', our Freddie steals a painting & kills a chambermaid; in 'Ghosts' he is released from prision and moves to a small island; and in 'Athena' he, well, falls in love. Perhaps. The first two are gorgeously rendered pieces, haunting (sorry, awful but unavoidable pun) yet compulsively readable despite their non-reliance on plot. I found 'Athena' harder to get into, perhaps because in the early parts Freddie (by this point living under another name) seems less present than the earlier two, even though he narrates all three. Still, the second half works better and it remains a worthy companion, and I suspect it will improve with re-reading.
Banville, in content, reminds me of Paul Auster & Milan Kundera, with the constant refractions of identity, art & the near-solitude of the main characters (though without the contemporary cultural references of either - Banville's characters always seem to live in a void in which the past exists but the present does not). In style, though, he is closest, as others have observed, to Vladimir Nabokov (though perhaps without as much a sense of playful puzzle-building). Most obviously this is manifest in his 'confessional narrative', unreliable narrators using their writing not so much to tell a story as to secure their own futures, allowing things to be remembered 'their' way. But I would also note that Nabokov and Banville are the two best users of brackets of any authors I have read - read any of the novels in this trilogy and Nabokov's 'Transparent Things', for instance, if you have ever doubted that a pair of brackets can be devastatingly employed. Anyone who has enjoyed any of these three authors' work would do well to investigate Banville, and this trilogy is as good a place as any to start.