LEADER 03638nam 22006375 450 001 9910146273703321 005 20250724090423.0 010 $a3-540-44563-3 024 7 $a10.1007/b55674 035 $a(CKB)1000000000437217 035 $a(SSID)ssj0000326651 035 $a(PQKBManifestationID)11266256 035 $a(PQKBTitleCode)TC0000326651 035 $a(PQKBWorkID)10297566 035 $a(PQKB)10406331 035 $a(DE-He213)978-3-540-44563-0 035 $a(MiAaPQ)EBC6296462 035 $a(MiAaPQ)EBC5591702 035 $a(Au-PeEL)EBL5591702 035 $a(OCoLC)1066189602 035 $a(PPN)155198092 035 $a(EXLCZ)991000000000437217 100 $a20121227d2001 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aSimilarity Problems and Completely Bounded Maps /$fby Gilles Pisier 205 $a2nd ed. 2001. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2001. 215 $a1 online resource (X, 202 p.) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v1618 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-540-41524-6 320 $aIncludes bibliographical references and index. 327 $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. 330 $aThese notes revolve around three similarity problems, appearing in three different contexts, but all dealing with the space B(H) of all bounded operators on a complex Hilbert space H. The first one deals with group representations, the second one with C* -algebras and the third one with the disc algebra. We describe them in detail in the introduction which follows. This volume is devoted to the background necessary to understand these three problems, to the solutions that are known in some special cases and to numerous related concepts, results, counterexamples or extensions which their investigation has generated. While the three problems seem different, it is possible to place them in a common framework using the key concept of "complete boundedness", which we present in detail. Using this notion, the three problems can all be formulated as asking whether "boundedness" implies "complete boundedness" for linear maps satisfying certain additional algebraic identities. Two chapters have been added on the HALMOS and KADISON similarity problems. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v1618 606 $aFunctional analysis 606 $aHarmonic analysis 606 $aFunctional Analysis 606 $aAbstract Harmonic Analysis 615 0$aFunctional analysis. 615 0$aHarmonic analysis. 615 14$aFunctional Analysis. 615 24$aAbstract Harmonic Analysis. 676 $a512.55 700 $aPisier$b Gilles$4aut$4http://id.loc.gov/vocabulary/relators/aut$049047 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910146273703321 996 $aSimilarity problems and completely bounded maps$978071 997 $aUNINA