Similarity Problems and Completely Bounded Maps / by Gilles Pisier.

Format:

Book

Author/Creator:

Pisier, Gilles, 1950- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1618.

Lecture Notes in Mathematics, 0075-8434 ; 1618

Language:

English

Subjects (All):

Distribution (Probability theory).

Probability Theory and Stochastic Processes.

Theoretical, Mathematical and Computational Physics.

Optics, Lasers, Photonics, Optical Devices.

Quantum Optics.

Local Subjects:

Probability Theory and Stochastic Processes.

Theoretical, Mathematical and Computational Physics.

Optics, Lasers, Photonics, Optical Devices.

Quantum Optics.

Physical Description:

1 online resource (VII, 160 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1996.

System Details:

text file PDF

Summary:

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.

Contents:

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.

Other Format:

Printed edition:

ISBN:

9783662215371

Access Restriction:

Restricted for use by site license.