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Hilbert Space : Compact Operators and the Trace Theorem - J. R. Retherford

Hilbert Space

Compact Operators and the Trace Theorem

Paperback Published: 6th September 1993
ISBN: 9780521429337
Number Of Pages: 144

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The aim of 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. The author assumes the reader is familiar with 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.

"Retherford's book...is like a tour to the top of a mountain. Every step is devoted to the final goal, the trace formula...the book is written in a style which reveals the author's enthusiasm. Thus it could be good prpaganda for functional analysis...this is a remarkable book which forces the student to understand mathematics and to be careful." A. Pietsch, Mathematical Reviews

Introductionp. xi
The inequalities of it allp. 1
Preliminariesp. 3
Orthogonalityp. 11
Isomorphisms and Isometriesp. 25
Bounded Linear Operators on Hilbert Spacep. 28
Elementary Spectral Theoryp. 36
Self-Adjoint Operatorsp. 49
Compact Operators on Hilbert Spacep. 60
Compact Integral Operatorsp. 69
Square Rootsp. 70
The Weak Weyl Inequalityp. 78
The Weyl Inequalityp. 87
Hilbert-Schmidt and Trace Class Operatorsp. 93
The Lidskij Trace Theoremp. 109
Localization of Eigenvaluesp. 124
Bibliographyp. 126
Index of Notationp. 127
Index of Termsp. 130
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521429337
ISBN-10: 0521429331
Series: London Mathematical Society Student Texts
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 144
Published: 6th September 1993
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 0.9
Weight (kg): 0.22