Hilbert space: compact operators and the trace theorem
Professor Retherford's aim in this book is to provide the reader with a virtually self-contained treatment of Hilbert space theory, leading to an elementary proof of the Lidskij trace theorem. He assumes the reader is familiar with only linear algebra and advanced calculus, and develops everything needed to introduce the ideas of compact, self-adjoint, Hilbert-Schmidt and trace class operators. Many exercises and hints are included, and throughout the emphasis is on a user-friendly approach. Ad…
Read More ↓Title Statements
- Full title :Hilbert space : compact operators and the trace theorem / J.R. Retherford.
Summary
Professor Retherford's aim in this book is to provide the reader with a virtually self-contained treatment of Hilbert space theory, leading to an elementary proof of the Lidskij trace theorem. He assumes the reader is familiar with only linear algebra and advanced calculus, and develops everything needed to introduce the ideas of compact, self-adjoint, Hilbert-Schmidt and trace class operators. Many exercises and hints are included, and throughout the emphasis is on a user-friendly approach. Advanced undergraduates and graduate students will find that this book presents a unique introduction to operators and Hilbert space.
Read More ↓Edition Statements
- Publication Date:©1993.
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge [England]
- Language:eng
- Publication Date:©1993.
The Physical Object
- Description:1 online resource (xii, 131 pages)
Edition Identifiers
- ISBN:9781139172592, 113917259X, 9781107088320, 1107088321
- oclc:ocn817977283
- LC Classification:QA322.4
- Dewey Decimal:515/.733
Table of Contents
Cover; Series Page; Title; Copyright; Dedication; ACKNOWLEDGEMENT; CONTENTS; INTRODUCTION; 0. THE INEQUALITIES OF IT ALL; I. PRELIMINARIES; Exercise 1. Read the introduction!; Remarks, Exercises and Hints; II. ORTHOGONALITY; Remarks, Exercises and Hints; III. ISOMORPHISMS AND ISOMETRIES; Remarks, Exercises and Hints; IV. BOUNDED LINEAR OPERATORS ON HILBERT SPACE; Remarks, Exercises, and Hints; V. ELEMENTARY SPECTRAL THEORY; Remarks, Exercises, Hints; VI. SELF-ADJOINT OPERATORS; Remarks, Exercises, and Hints; VII. COMPACT OPERATORS; Remarks, Exercises and Hints
APPENDIX A: COMPACT INTEGRAL OPERATORSVIII. SQUARE ROOTS; Remarks, Exercises, and Hints; IX. THE WEAK WEYL INEQUALITY; APPENDIX B: THE WEYL INEQUALITY; Remarks, Exercises and Hints; X. IDLBERT-SCHMIDT AND TRACE CLASS OPERATORS; Remarks, Exercises and Hints; XI. THE LIDSKIJ TRACE THEOREM; Final Remarks, Exercises and Hints; APPENDIX C: LOCALIZATION OF EIGENVALUES; BIBLIOGRAPHY; Books; Research Papers; Future Reading; INDEX OF NOTATION; INDEX OF TERMS
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