Trace ideals and their applications / Barry Simon.

Format:

Book

Author/Creator:

Simon, Barry, 1946- author.

Series:

Mathematical surveys and monographs ; no. 120.

Mathematical surveys and monographs ; volume 120

Language:

English

Subjects (All):

Operator theory.

Hilbert space.

Ideals (Algebra).

Mathematical physics.

Physical Description:

1 online resource (162 p.)

Edition:

2nd ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2005]

Language Note:

English

Summary:

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 This is a second edition of a well-known book 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 second 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.

Contents:

""Contents""; ""Preface to the Second Edition""; ""Preface to the First Edition""; ""Chapter 1. Preliminaries""; ""1.1. Absolute Value and Polar Decomposition""; ""1.2. Compact Operators and the Canonical Decomposition""; ""1.3. Inequalities on Singular Values, I""; ""1.4. Rearrangement Inequalities and All That""; ""1.5. Antisymmetric Tensor Products""; ""1.6. Inequalities on Eigenvalues, I""; ""1.7. Symmetrically Normed Spaces""; ""1.8. Inequalities on Singular Values and Eigenvalues, II""; ""1.9. Clarkson-McCarthy Inequalities""

""Chapter 2. Calkin's Theory of Operator Ideals and Symmetrically Normed Ideals Convergence Theorems for J[sub(p)]""; ""Chapter 3. Trace, Determinant, and Lidskii's Theorem""; ""Chapter 4. f(x)g(�iV)""; ""Chapter 5. Fredholm Theory""; ""Chapter 6. Scattering With a Trace Condition""; ""Chapter 7. Bound State Problems""; ""Chapter 8. Lots of Inequalities""; ""8.1. Golden-Thompson Inequalities""; ""8.2. Lieb's Inequalities""; ""8.3. Peierls-Bogoliubov and Berezin Inequalities""; ""8.4. Lieb Concavity""; ""Chapter 9. Regularized Determinants and Renormalization in Quantum Field Theory""

""Chapter 10. An Introduction to the Theory on a Banach Space""""Chapter 11. Borel Transforms, the Krein Spectral Shift, and All That""; ""11.1. Borel Transforms of Measures""; ""11.2. Rank One Perturbations: The Set-Up and Basic Formulae""; ""11.3. The Integral Formula""; ""11.4. The Krein Spectral Shift""; ""Appendix to Section 11.4: The Krein Spectral Shift for Trace Class Perturbations""; ""11.5. Infinite Coupling""; ""11.6. Boundary Condition Variation of ODE's""; ""11.7. Jacobi Matrices""; ""Chapter 12. Spectral Theory of Rank One Perturbations""

""Index""""A""; ""B""; ""C""; ""D""; ""F""; ""G""; ""H""; ""I""; ""J""; ""K""; ""L""; ""M""; ""N""; ""P""; ""R""; ""S""; ""T""; ""U""; ""W""; ""X""; ""Y""

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 135-136) and index.

Description based on print version record.

ISBN:

1-4704-1347-7