**Mathematical Surveys and Monographs**

Volume: 120;
2005;
150 pp;
Softcover

MSC: Primary 47;
Secondary 81

**Print ISBN: 978-0-8218-4988-0
Product Code: SURV/120.S**

List Price: $61.00

AMS Member Price: $48.80

MAA Member Price: $54.90

**Electronic ISBN: 978-1-4704-1347-7
Product Code: SURV/120.S.E**

List Price: $57.00

AMS Member Price: $45.60

MAA Member Price: $51.30

#### Supplemental Materials

# Trace Ideals and Their Applications: Second Edition

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*Barry Simon*

This is a second edition of a well-known book stemming from
the author's lectures on the theory of trace ideals in the algebra of
operators in a Hilbert space. Because of the theory's many different
applications, the book was widely used and much in demand.

For this edition, the author has added four chapters on the
closely related theory of rank one perturbations of self-adjoint
operators. He has also included a comprehensive index and an addendum
describing some developments since the original notes were
published.

This book continues to be a vital source of information for those
interested in the theory of trace ideals and in its applications to
various areas of mathematical physics.

#### Readership

Graduate students and research mathematicians interested in the theory of operators and its applications to mathematical physics.

#### Reviews & Endorsements

...very well suited for a graduate course since the exposition is clear and perfectly self-contained.

-- Mathematical Reviews

Beautifully written and well organized ... indispensable for those interested in certain areas of mathematical physics ... for the expert and beginner alike. The author deserves to be congratulated both for his work in unifying a subject and for showing workers in the field new directions for future development.

-- Zentralblatt MATH

#### Table of Contents

# Table of Contents

## Trace Ideals and Their Applications: Second Edition

- Contents iii4 free
- Preface to the Second Edition v6 free
- Preface to the First Edition vii8 free
- Chapter 1. Preliminaries 110 free
- 1.1. Absolute Value and Polar Decomposition 110
- 1.2. Compact Operators and the Canonical Decomposition 110
- 1.3. Inequalities on Singular Values, I 312
- 1.4. Rearrangement Inequalities and All That 413
- 1.5. Antisymmetric Tensor Products 615
- 1.6. Inequalities on Eigenvalues, I 817
- 1.7. Symmetrically Normed Spaces 817
- 1.8. Inequalities on Singular Values and Eigenvalues, II 1120
- 1.9. Clarkson-McCarthy Inequalities 1423

- Chapter 2. Calkin's Theory of Operator Ideals and Symmetrically Normed Ideals; Convergence Theorems for J[sub(p)] 1726
- Chapter 3. Trace, Determinant, and Lidskii's Theorem 3140
- Chapter 4. f(x)g( i∇) 3746
- Chapter 5. Fredholm Theory 4554
- Chapter 6. Scattering With a Trace Condition 5362
- Chapter 7. Bound State Problems 6170
- Chapter 8. Lots of Inequalities 6776
- Chapter 9. Regularized Determinants and Renormalization in Quantum Field Theory 7584
- Chapter 10. An Introduction to the Theory on a Banach Space 8190
- Chapter 11. Borel Transforms, the Krein Spectral Shift, and All That 8594
- Chapter 12. Spectral Theory of Rank One Perturbations 105114
- Chapter 13. Localization in the Anderson Model Following Aizenman-Molchanov 113122
- Chapter 14. The Xi Function 117126
- Appendix. Addenda 127136
- Bibliography 135144
- Index 149158