Hilbert Space
Compact Operators and the Trace Theorem

A virtually self-contained treatment of Hilbert space theory which is suitable for advanced undergraduates and graduate students.

J. R. Retherford (Author)

9780521418843, Cambridge University Press

Hardback, published 8 July 1993

144 pages
23.5 x 15.9 x 1.6 cm, 0.37 kg

"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

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.

1. Preliminaries
2. Orthogonality
3. Isomorphisms and isometries
4. Bounded linear operators
5. Elementary spectral theory
6. Self-adjoint operators
7. Compact operators on Hilbert space
8. Square roots
9. The weak Weyl inequality
10. Hilbert–Schmidt and trace class operators
11. The Lidskij trace theorem
Bibliography.

Subject Areas: Calculus & mathematical analysis [PBK]