A Hilbert Space Problem Book / by P.R. Halmos.

Format:

Book

Author/Creator:

Halmos, Paul R. (Paul Richard), 1916-2006, author.

Contributor:

SpringerLink (Online service)

Series:

Graduate texts in mathematics 2197-5612 ; 19.

Graduate Texts in Mathematics, 2197-5612 ; 19

Language:

English

Subjects (All):

Mathematical analysis.

Analysis.

Local Subjects:

Analysis.

Physical Description:

1 online resource.

Edition:

First edition 1974.

Contained In:

Springer Nature eBook

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 1974.

System Details:

text file PDF

Summary:

From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks... The second part, a very short one, consists of hints... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem.... This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book.".

Contents:

Problem

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

Hint

Solution

References.

Other Format:

Printed edition:

ISBN:

9781461599760

Access Restriction:

Restricted for use by site license.