TY  - BOOK
AU  - Pisier,Gilles
ED  - SpringerLink (Online service)
TI  - Similarity Problems and Completely Bounded Maps
T2  - Lecture Notes in Mathematics,
SN  - 9783662215371
AV  - QA273.A1-274.9 
U1  - 519.2 23
PY  - 1996///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg, Imprint: Springer
KW  - Mathematics
KW  - Distribution (Probability theory)
KW  - Probability Theory and Stochastic Processes
KW  - Theoretical, Mathematical and Computational Physics
KW  - Laser Technology, Photonics
KW  - Quantum Optics
N1  - 0. 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
N2  - This 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
UR  - http://dx.doi.org/10.1007/978-3-662-21537-1
ER  -