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  • Textbook
  • © 1982

A Hilbert Space Problem Book

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 19)

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  • ISBN: 978-1-4684-9330-6
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Table of contents (75 chapters)

  1. Front Matter

    Pages i-xvii
  2. Problems

    1. Front Matter

      Pages 1-1
    2. Vectors

      • Paul R. Halmos
      Pages 3-8
    3. Spaces

      • Paul R. Halmos
      Pages 9-11
    4. Weak Topology

      • Paul R. Halmos
      Pages 12-16
    5. Analytic Functions

      • Paul R. Halmos
      Pages 17-22
    6. Infinite Matrices

      • Paul R. Halmos
      Pages 23-26
    7. Boundedness and Invertibility

      • Paul R. Halmos
      Pages 27-32
    8. Multiplication Operators

      • Paul R. Halmos
      Pages 33-37
    9. Operator Matrices

      • Paul R. Halmos
      Pages 38-40
    10. Properties of Spectra

      • Paul R. Halmos
      Pages 41-43
    11. Examples of Spectra

      • Paul R. Halmos
      Pages 44-46
    12. Spectral Radius

      • Paul R. Halmos
      Pages 47-53
    13. Norm Topology

      • Paul R. Halmos
      Pages 54-58
    14. Operator Topologies

      • Paul R. Halmos
      Pages 59-62
    15. Strong Operator Topology

      • Paul R. Halmos
      Pages 63-65
    16. Partial Isometries

      • Paul R. Halmos
      Pages 66-73
    17. Polar Decomposition

      • Paul R. Halmos
      Pages 74-76
    18. Unilateral Shift

      • Paul R. Halmos
      Pages 77-85
    19. Cyclic Vectors

      • Paul R. Halmos
      Pages 86-89

About this book

From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks... The second part, a very short one, consists of hints... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem....

This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book."

Keywords

  • Finite
  • Hilbertscher Raum
  • Isometrie
  • Space
  • Topology
  • function
  • proof

Bibliographic Information

  • Book Title: A Hilbert Space Problem Book

  • Authors: Paul R. Halmos

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4684-9330-6

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1982

  • Hardcover ISBN: 978-0-387-90685-0

  • eBook ISBN: 978-1-4684-9330-6

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 2

  • Number of Pages: XVII, 373

  • Topics: Differential Geometry

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • ISBN: 978-1-4684-9330-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book USD 109.99
Price excludes VAT (USA)