Hilbert space : compact operators and the trace theorem / J.R. Retherford.

Includes bibliographical references (page 126) and index.

Print version record.

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.

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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