Softcover ISBN:  9780821849880 
Product Code:  SURV/120.S 
List Price:  $61.00 
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AMS Member Price:  $48.80 
Electronic ISBN:  9781470413477 
Product Code:  SURV/120.S.E 
List Price:  $57.00 
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Book DetailsMathematical Surveys and MonographsVolume: 120; 2005; 150 ppMSC: Primary 47; Secondary 81;
This is a second edition of a wellknown 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 selfadjoint 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.ReadershipGraduate students and research mathematicians interested in the theory of operators and its applications to mathematical physics.

Table of Contents

Chapters

1. Preliminaries

2. Calkin’s theory of operator ideals and symmetrically normed ideals; convergence theorems for $\mathcal {J}_P$

3. Trace, determinant, and Lidskii’s theorem

4. $f(x)g(i\nabla )$

5. Fredholm theory

6. Scattering with a trace condition

7. Bound state problems

8. Lots of inequalities

9. Regularized determinants and renormalization in quantum field theory

10. An introduction to the theory on a Banach space

11. Borel transforms, the Krein spectral shift, and all that

12. Spectral theory of rank one perturbations

13. Localization in the Anderson model following AizenmanMolchanov

14. The Xi function


Additional Material

Reviews

...very well suited for a graduate course since the exposition is clear and perfectly selfcontained.
Mathematical Reviews 
From a review of the first edition: 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


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This is a second edition of a wellknown 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 selfadjoint 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.
Graduate students and research mathematicians interested in the theory of operators and its applications to mathematical physics.

Chapters

1. Preliminaries

2. Calkin’s theory of operator ideals and symmetrically normed ideals; convergence theorems for $\mathcal {J}_P$

3. Trace, determinant, and Lidskii’s theorem

4. $f(x)g(i\nabla )$

5. Fredholm theory

6. Scattering with a trace condition

7. Bound state problems

8. Lots of inequalities

9. Regularized determinants and renormalization in quantum field theory

10. An introduction to the theory on a Banach space

11. Borel transforms, the Krein spectral shift, and all that

12. Spectral theory of rank one perturbations

13. Localization in the Anderson model following AizenmanMolchanov

14. The Xi function

...very well suited for a graduate course since the exposition is clear and perfectly selfcontained.
Mathematical Reviews 
From a review of the first edition: 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