A Primer on Hilbert Space Operators

  • Piotr Sołtan

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

Table of contents

  1. Front Matter
    Pages i-xii
  2. Bounded Operators

    1. Front Matter
      Pages 1-1
    2. Piotr Sołtan
      Pages 3-12
    3. Piotr Sołtan
      Pages 13-18
    4. Piotr Sołtan
      Pages 19-31
    5. Piotr Sołtan
      Pages 33-57
    6. Piotr Sołtan
      Pages 59-67
    7. Piotr Sołtan
      Pages 69-86
  3. Unbounded Operators

    1. Front Matter
      Pages 99-99
    2. Piotr Sołtan
      Pages 101-111
    3. Piotr Sołtan
      Pages 113-127
    4. Piotr Sołtan
      Pages 129-144
    5. Piotr Sołtan
      Pages 165-173
  4. Back Matter
    Pages 175-200

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.


hilbert space bounded operator unbounded operator C*-algebra functional calculus z-transform

Authors and affiliations

  • Piotr Sołtan
    • 1
  1. 1.Faculty of PhysicsUniversity of WarsawWarsawPoland

Bibliographic information