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A Hilbert space problem book

Author: Paul R Halmos
Publisher: Princeton, N.J., Van Nostrand [1967]
Series: University series in higher mathematics.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
The purpose of this book is to use problems and their solutions to communicate to the reader many of the central techniques and ideas of Hilbert spaces. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks. Most of the problems are statements to be proved, but some are questions, and some are challenges. The second part,  Read more...
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Genre/Form: Aufgabensammlung
Problems and exercises
Problems, exercises, etc
Additional Physical Format: Online version:
Halmos, Paul R. (Paul Richard), 1916-2006.
Hilbert space problem book.
Princeton, N.J., Van Nostrand [1967]
(OCoLC)567903465
Online version:
Halmos, Paul R. (Paul Richard), 1916-2006.
Hilbert space problem book.
Princeton, N.J., Van Nostrand [1967]
(OCoLC)609824849
Document Type: Book
All Authors / Contributors: Paul R Halmos
OCLC Number: 527924
Description: xvii, 365 pages 24 cm.
Contents: 1. Vectors and spaces --
2. Weak topology --
3. Analytic functions --
4. Infinite matrices --
5. Boundedness and invertibility --
6. Multiplication operators --
7. Operator matrices --
8. Properties of spectra --
9. Examples of spectra --
10. Spectral radius --
11. Norm topology --
12. Strong and weak topologies --
13. Partial isometries --
14. Unilateral shift --
15. Compact operators --
16. Subnormal operators --
17. Numerical range --
18. Unitary dilations --
19. Commutators of operators --
20. Toeplitz operators.
Series Title: University series in higher mathematics.
Responsibility: [by] Paul R. Halmos.

Abstract:

The purpose of this book is to use problems and their solutions to communicate to the reader many of the central techniques and ideas of Hilbert spaces. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks. Most of the problems are statements to be proved, but some are questions, and some are challenges. The second part, a very short one, consists of hints. The third part consists of solutions: proofs, answers, or constructions, depending on the nature of the problem. The solution may also introduce standard nomenclature, discuss the history of the subject, and mention pertinent references.--

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