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A Primer on Hilbert Space Operators

  • Textbook
  • © 2018

Overview

Authors:
  1. Piotr Sołtan

    1. Faculty of Physics, University of Warsaw, Warsaw, Poland

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  • Provides a quick insight into the theory of operators on Hilbert spaces
  • Thorough and self-contained presentation
  • Highlight: Presentation of the z-transform to deal with unbounded operators

Part of the book series: Compact Textbooks in Mathematics (CTM)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xii
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  2. Bounded Operators

    1. Front Matter

      Pages 1-1
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    2. Spectrum of an Operator

      • Piotr Sołtan
      Pages 3-12

    3. Continuous Functional Calculus

      • Piotr Sołtan
      Pages 13-18

    4. Positive Operators

      • Piotr Sołtan
      Pages 19-31

    5. Spectral Theorems and Functional Calculus

      • Piotr Sołtan
      Pages 33-57

    6. Compact Operators

      • Piotr Sołtan
      Pages 59-67

    7. The Trace

      • Piotr Sołtan
      Pages 69-86

    8. Functional Calculus for Families of Operators

      • Piotr Sołtan
      Pages 87-97

  3. Unbounded Operators

    1. Front Matter

      Pages 99-99
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    2. Operators and Their Graphs

      • Piotr Sołtan
      Pages 101-111

    3. z-Transform

      • Piotr Sołtan
      Pages 113-127

    4. Spectral Theorems

      • Piotr Sołtan
      Pages 129-144

    5. Self-Adjoint Extensions of Symmetric Operators

      • Piotr Sołtan
      Pages 145-163

    6. One-Parameter Groups of Unitary Operators

      • Piotr Sołtan
      Pages 165-173

  4. Back Matter

    Pages 175-200
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Keywords

About this book

The book concisely presents the fundamental aspects of the theory of operators on Hilbert spaces. The topics covered include functional calculus and spectral theorems, compact operators, trace class and Hilbert-Schmidt operators, self-adjoint extensions of symmetric operators, and one-parameter groups of operators.

The exposition of the material on unbounded operators is based on a novel tool, called the z-transform, which provides a way to encode full information about unbounded operators in bounded ones, hence making many technical aspects of the theory less involved.

Reviews

“We warmly recommend the book to students interested in operator theory and many of its significant applications.” (Valentin Keyantuo, Mathematical Reviews, November, 2019)

“The book under review is a solid and concise textbook for advanced undergraduate and masters students. ... It is all in all an excellent book and the reviewer would definitely recommend it to anybody who wants to learn the theory of (bounded as well as unbounded) linear operators on Hilbert spaces.” (Jaydeb Sarkar, zbMath 1417.47001, 2019)


Authors and Affiliations

  • Faculty of Physics, University of Warsaw, Warsaw, Poland

    Piotr Sołtan

About the author

Piotr ​Sołtan 

Bibliographic Information

  • Book Title: A Primer on Hilbert Space Operators

  • Authors: Piotr Sołtan

  • Series Title: Compact Textbooks in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-92061-0

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2018

  • Softcover ISBN: 978-3-319-92060-3Published: 17 September 2018

  • eBook ISBN: 978-3-319-92061-0Published: 04 September 2018

  • Series ISSN: 2296-4568

  • Series E-ISSN: 2296-455X

  • Edition Number: 1

  • Number of Pages: XII, 200

  • Number of Illustrations: 1 illustrations in colour

  • Topics: Operator Theory

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