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  • © 2003

Means of Hilbert Space Operators

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-VIII
  2. 1 Introduction

    • Fumio Hiai, Hideki Kosaki
    Pages 1-6
  3. 2 Double integral transformations

    • Fumio Hiai, Hideki Kosaki
    Pages 7-32
  4. 3 Means of operators and their comparison

    • Fumio Hiai, Hideki Kosaki
    Pages 33-55
  5. 4 Convergence of means

    • Fumio Hiai, Hideki Kosaki
    Pages 57-63
  6. 5 A-L-G interpolation means M α

    • Fumio Hiai, Hideki Kosaki
    Pages 65-78
  7. 6 Heinz-type means A α

    • Fumio Hiai, Hideki Kosaki
    Pages 79-87
  8. 7 Binomial means B α

    • Fumio Hiai, Hideki Kosaki
    Pages 89-104
  9. 8 Certain alternating sums of operators

    • Fumio Hiai, Hideki Kosaki
    Pages 105-121
  10. A Appendices

    • Fumio Hiai, Hideki Kosaki
    Pages 123-139
  11. References

    • Fumio Hiai, Hideki Kosaki
    Pages 141-144
  12. Back Matter

    Pages 145-148

About this book

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
  • matrix theory

Bibliographic Information

  • Book Title: Means of Hilbert Space Operators

  • Authors: Fumio Hiai, Hideki Kosaki

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b13213

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2003

  • Softcover ISBN: 978-3-540-40680-8Published: 19 August 2003

  • eBook ISBN: 978-3-540-45152-5Published: 09 December 2003

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 156

  • Topics: Functional Analysis, Operator Theory, Linear Algebra

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions