Hilbert space : compact operators and the trace theorem
著者
書誌事項
Hilbert space : compact operators and the trace theorem
（London Mathematical Society student texts, 27）
Cambridge University Press, 1993
- : hbk
- : pbk
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注記
Includes bibliographical references (p. [126]) and indexes
内容説明・目次
内容説明
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.
目次
- 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.
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