A Primer on Hilbert Space Operators

✍ Scribed by Piotr Sołtan

• Publisher: Springer International Publishing;Birkhäuser
• Year: 2018
• Tongue: English
• Leaves: 200
• Series: Compact Textbooks in Mathematics
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xii
Front Matter ....Pages 1-1
Spectrum of an Operator (Piotr Sołtan)....Pages 3-12
Continuous Functional Calculus (Piotr Sołtan)....Pages 13-18
Positive Operators (Piotr Sołtan)....Pages 19-31
Spectral Theorems and Functional Calculus (Piotr Sołtan)....Pages 33-57
Compact Operators (Piotr Sołtan)....Pages 59-67
The Trace (Piotr Sołtan)....Pages 69-86
Functional Calculus for Families of Operators (Piotr Sołtan)....Pages 87-97
Front Matter ....Pages 99-99
Operators and Their Graphs (Piotr Sołtan)....Pages 101-111
z-Transform (Piotr Sołtan)....Pages 113-127
Spectral Theorems (Piotr Sołtan)....Pages 129-144
Self-Adjoint Extensions of Symmetric Operators (Piotr Sołtan)....Pages 145-163
One-Parameter Groups of Unitary Operators (Piotr Sołtan)....Pages 165-173
Back Matter ....Pages 175-200

✦ Subjects

Mathematics; Operator Theory