000 03470nam a22005175i 4500
001 978-3-662-21537-1
003 DE-He213
005 20160624101838.0
007 cr nn 008mamaa
008 130609s1996 gw | s |||| 0|eng d
020 _a9783662215371
_9978-3-662-21537-1
024 7 _a10.1007/978-3-662-21537-1
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aPisier, Gilles.
_eauthor.
245 1 0 _aSimilarity Problems and Completely Bounded Maps
_h[electronic resource] /
_cby Gilles Pisier.
260 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1996.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1996.
300 _aVII, 160 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 _a0. Introduction. Description of contents -- 1. Von Neumann’s inequality and Ando’s generalization -- 2. Non-unitarizable uniformly bounded group representations -- 3. Completely bounded maps -- 4. Completely bounded homomorphisms and derivations -- 5. Schur multipliers and Grothendieck’s inequality -- 6. Hankelian Schur multipliers. Herz-Schur multipliers -- 7. The similarity problem for cyclic homomorphisms on a C*-algebra -- 8. Completely bounded maps in the Banach space setting -- References -- Notation Index.
520 _aThis book is mainly about 3 similarity problems arising in 3 different contexts, namely group representations,C*-algebras and uniform algebras (eg. the disc algebra). These 3 problems (all still open in full generality) are studied using a common tool, completely bounded maps, which have recently emerged as a major concept in operator algebra theory. The book is devoted to the background necessary to understand these problems, to the partial solutions that are known and to numerous related concepts, results, counterexamples or extensions. The variety of topics involved, ranging from functional analysis to harmonic analysis, Hp-spaces, Fourier multipliers, Schur multipliers, coefficients of group representations, group algebras, characterizations of amenable groups, nuclear C*-algebras, Hankel operators, etc, is an attraction of this book. It is mostly self-contained and accessible to graduate students mastering basic functional and harmonic analysis. For more advanced readers, it can be an invitation to the recently developed theory of "operator spaces", for which completely bounded maps are the fundamental morphisms.
650 0 _aMathematics.
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aTheoretical, Mathematical and Computational Physics.
650 2 4 _aLaser Technology, Photonics.
650 2 4 _aQuantum Optics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540603221
786 _dSpringer
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1618
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-662-21537-1
942 _2EBK2028
_cEBK
999 _c31322
_d31322