Contents Preface to the Second Edition v Preface to the First Edition vii Chapter 1. Preliminaries 1 1.1. Absolute Value and Polar Decomposition 1 1.2. Compact Operators and the Canonical Decomposition 1 1.3. Inequalities on Singular Values, I 3 1.4. Rearrangement Inequalities and All That 4 1.5. Antisymmetric Tensor Products 6 1.6. Inequalities on Eigenvalues, I 8 1.7. Symmetrically Normed Spaces 8 1.8. Inequalities on Singular Values and Eigenvalues, II 11 1.9. Clarkson-McCarthy Inequalities 14 Chapter 2. Calkin's Theory of Operator Ideals and Symmetrically Normed Ideals Convergence Theorems for Jp 17 Chapter 3. Trace, Determinant, and Lidskii's Theorem 31 Chapter 4. f(x)g(~iV) 37 Chapter 5. Fredholm Theory 45 Chapter 6. Scattering With a Trace Condition 53 Chapter 7. Bound State Problems 61 Chapter 8. Lots of Inequalities 67 8.1. Golden-Thompson Inequalities 67 8.2. Lieb's Inequalities 70 8.3. Peierls-Bogoliubov and Berezin Inequalities 71 8.4. Lieb Concavity 72 Chapter 9. Regularized Determinants and Renormalization in Quantum Field Theory 75 Chapter 10. An Introduction to the Theory on a Banach Space 81 Chapter 11. Borel Transforms, the Krein Spectral Shift, and All That 85 11.1. Borel Transforms of Measures 86 11.2. Rank One Perturbations: The Set-Up and Basic Formulae 90
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