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- catalog abstract "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.".
- catalog contributor b8822080.
- catalog created "c1996.".
- catalog date "1996".
- catalog date "c1996.".
- catalog dateCopyrighted "c1996.".
- catalog description "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.".
- catalog description "Includes bibliographical references (p. [143]-151) and indexes.".
- catalog description "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.".
- catalog extent "vi, 156 p. ;".
- catalog hasFormat "Similarity problems and completely bounded maps.".
- catalog identifier "3540603220 (pbk. : alk. paper)".
- catalog isFormatOf "Similarity problems and completely bounded maps.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1618.".
- catalog isPartOf "Lecture notes in mathematics ; 1618".
- catalog issued "1996".
- catalog issued "c1996.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer,".
- catalog relation "Similarity problems and completely bounded maps.".
- catalog subject "510 s 512/.55 20".
- catalog subject "C*-algebras.".
- catalog subject "Distribution (Probability theory).".
- catalog subject "Linear operators.".
- catalog subject "Mappings (Mathematics)".
- catalog subject "Mathematics.".
- catalog subject "QA3 .L28 no. 1618 QA329.2".
- catalog subject "Representations of groups.".
- catalog tableOfContents "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.".
- catalog title "Similarity problems and completely bounded maps / Gilles Pisier.".
- catalog type "text".