Similarity Problems and Completely Bounded Maps

  • Gilles Pisier

Part of the Lecture Notes in Mathematics book series (LNM, volume 1618)

Table of contents

  1. Front Matter
    Pages N2-vii
  2. Gilles Pisier
    Pages 1-12
  3. Gilles Pisier
    Pages 53-69
  4. Back Matter
    Pages 143-161

About this book

Introduction

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.

Keywords

42B30 43A65 46E40 46L05 46L57 47A05 47A20 47B10 47C15 47L20 Completely bounded representation H (p) spaces Harmonic analysis Polynomially bounded operator operator algebras similar to contraction similar to unitary uniformly bounded representation operator algebra solution

Authors and affiliations

  • Gilles Pisier
    • 1
    • 2
  1. 1.Mathematics DepartmentTexas A&M UniversityCollege StationUSA
  2. 2.Equipe d’AnalyseUniversité Paris VIParis Cedex 05France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-21537-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1996
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-60322-1
  • Online ISBN 978-3-662-21537-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book
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