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Similarity Problems and Completely Bounded Maps

  • Book
  • © 2001

Overview

Authors:
  1. Gilles Pisier
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  • Two chapters have been added on the HALMOS and KADISON similarity problems
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-vii
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  2. 0. Introduction. Description of contents

    • Gilles Pisier
    Pages 1-13

  3. 1. Von Neumann’s inequality and Ando’s generalization

    • Gilles Pisier
    Pages 14-30

  4. 2. Non-unitarizable uniformly bounded group representations

    • Gilles Pisier
    Pages 31-57

  5. 3. Completely bounded maps

    • Gilles Pisier
    Pages 58-74

  6. 4. Completely bounded homomorphisms and derivations

    • Gilles Pisier
    Pages 75-98

  7. 5. Schur multipliers and Grothendieck’s inequality

    • Gilles Pisier
    Pages 99-113

  8. 6. Hankelian Schur multipliers. Herz-Schur multipliers

    • Gilles Pisier
    Pages 114-123

  9. 7. The similarity problem for cyclic homomorphisms on a C*-algebra

    • Gilles Pisier
    Pages 124-141

  10. 8. Completely bounded maps in the Banach space setting

    • Gilles Pisier
    Pages 142-151

  11. 9. The Sz.-Nagy-Halmos similarity problem

    • Gilles Pisier
    Pages 152-167

  12. 10. The Kadison Similarity Problem

    • Gilles Pisier
    Pages 168-181

  13. References

    • Gilles Pisier
    Pages 182-193

  14. Subject and Notation Index

    • Gilles Pisier
    Pages 194-198

  15. Back Matter

    Pages 199-201
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Keywords

About this book

These notes revolve around three similarity problems, appearing in three different contexts, but all dealing with the space B(H) of all bounded operators on a complex Hilbert space H. The first one deals with group representations, the second one with C* -algebras and the third one with the disc algebra. We describe them in detail in the introduction which follows. This volume is devoted to the background necessary to understand these three problems, to the solutions that are known in some special cases and to numerous related concepts, results, counterexamples or extensions which their investigation has generated. While the three problems seem different, it is possible to place them in a common framework using the key concept of "complete boundedness", which we present in detail. Using this notion, the three problems can all be formulated as asking whether "boundedness" implies "complete boundedness" for linear maps satisfying certain additional algebraic identities.

Bibliographic Information

  • Book Title: Similarity Problems and Completely Bounded Maps

  • Authors: Gilles Pisier

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b55674

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2001

  • Softcover ISBN: 978-3-540-41524-4Published: 27 February 2001

  • eBook ISBN: 978-3-540-44563-0Published: 12 October 2004

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 2

  • Number of Pages: VII, 202

  • Topics: Functional Analysis, Abstract Harmonic Analysis

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