Means of Hilbert Space Operators

  • Authors
  • Fumio Hiai
  • Hideki Kosaki

Part of the Lecture Notes in Mathematics book series (LNM, volume 1820)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Fumio Hiai, Hideki Kosaki
    Pages 1-6
  3. Fumio Hiai, Hideki Kosaki
    Pages 7-32
  4. Fumio Hiai, Hideki Kosaki
    Pages 33-55
  5. Fumio Hiai, Hideki Kosaki
    Pages 57-63
  6. Fumio Hiai, Hideki Kosaki
    Pages 65-78
  7. Fumio Hiai, Hideki Kosaki
    Pages 79-87
  8. Fumio Hiai, Hideki Kosaki
    Pages 89-104
  9. Fumio Hiai, Hideki Kosaki
    Pages 105-121
  10. Fumio Hiai, Hideki Kosaki
    Pages 123-139
  11. Fumio Hiai, Hideki Kosaki
    Pages 141-144
  12. Back Matter
    Pages 145-148

About this book

Introduction

The monograph is devoted to a systematic study of means of Hilbert space operators by a unified method based on the theory of double integral transformations and Peller's characterization of Schur multipliers. General properties on means of operators such as comparison results, norm estimates and convergence criteria are established. After some general theory, special investigations are focused on three one-parameter families of A-L-G (arithmetic-logarithmic-geometric) interpolation means, Heinz-type means and binomial means. In particular, norm continuity in the parameter is examined for such means. Some necessary technical results are collected as appendices.

Keywords

Hilbert space Hilbert space operator Interpolation Schur multiplier double integral transformation integral transform mean of operators unitarily invariant norm

Bibliographic information

  • DOI https://doi.org/10.1007/b13213
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-40680-8
  • Online ISBN 978-3-540-45152-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book