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

Format:

Book

Author/Creator:

Retherford, J. R.

Series:

London Mathematical Society student texts ; 27.

London mathematical society student texts ; 27

Language:

English

Subjects (All):

Hilbert space.

Physical Description:

xii, 131 pages ; 24 cm.

Place of Publication:

Cambridge [England] ; New York, NY : Cambridge University Press, [1993]

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-ajoint, Hilbert-Schmidt and trace class operators.

Many exercises and hints are included, and the emphasis throughout 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.

Contents:

Chapter 0 The inequalities of it all 1

Chapter II Orthogonality 11

Chapter III Isomorphisms and Isometries 25

Chapter IV Bounded Linear Operators on Hilbert Space 28

Chapter V Elementary Spectral Theory 36

Chapter VI Self-Adjoint Operators 49

Chapter VII Compact Operators on Hilbert Space 60

Appendix A Compact Integral Operators 69

Chapter VIII Square Roots 70

Chapter IX The Weak Weyl Inequality 78

Appendix B The Weyl Inequality 87

Chapter X Hilbert-Schmidt and Trace Class Operators 93

Chapter XI The Lidskij Trace Theorem 109

Appendix C Localization of Eigenvalues 124.

Notes:

Includes bibliographical references (page 126) and index.

ISBN:

0521418844 :

0521429331

OCLC:

28388333