000 03493nam a22004935i 4500
001 978-3-540-44563-0
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007 cr nn 008mamaa
008 121227s2001 gw | s |||| 0|eng d
020 _a9783540445630
_9978-3-540-44563-0
024 7 _a10.1007/b55674
_2doi
050 4 _aQA319-329.9
072 7 _aPBKF
_2bicssc
072 7 _aMAT037000
_2bisacsh
072 7 _aPBKF
_2thema
082 0 4 _a515.7
_223
100 1 _aPisier, Gilles.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aSimilarity Problems and Completely Bounded Maps
_h[electronic resource] :
_bSecond, Expanded Edition /
_cby Gilles Pisier.
246 3 _aIncludes the solution to "The Halmos Problem"
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2001.
300 _aVII, 202 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1618
505 0 _aIntroduction. Description of contents -- Von Neumann's inequality and Ando's generalization -- Non-unitarizable uniformly bounded group representations -- Completely bounded maps -- Completely bounded homomorphisms and derivations -- Schur multipliers and Grothendieck's inequality -- Hankelian Schur multipliers. Herz-Schur multipliers -- The similarity problem for cyclic homomorphisms on a C*-algebra -- Completely bounded maps in the Banach space setting -- The Sz -- Nagy-Halmos similarity problem -- The Kadison Similarity Problem -- References -- Subject Index -- Notation Index.
520 _aThese notes revolve around three similarity problems, appearing in three different contexts, but all dealing with the space B(H) of all bounded operators on a complex Hilbert space H. The first one deals with group representations, the second one with C* -algebras and the third one with the disc algebra. We describe them in detail in the introduction which follows. This volume is devoted to the background necessary to understand these three problems, to the solutions that are known in some special cases and to numerous related concepts, results, counterexamples or extensions which their investigation has generated. While the three problems seem different, it is possible to place them in a common framework using the key concept of "complete boundedness", which we present in detail. Using this notion, the three problems can all be formulated as asking whether "boundedness" implies "complete boundedness" for linear maps satisfying certain additional algebraic identities. Two chapters have been added on the HALMOS and KADISON similarity problems.
650 0 _aFunctional analysis.
650 0 _aHarmonic analysis.
650 1 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
650 2 4 _aAbstract Harmonic Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12015
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662195246
776 0 8 _iPrinted edition:
_z9783540415244
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1618
856 4 0 _uhttps://doi.org/10.1007/b55674
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c9824
_d9824