Frontmatter -- Foreword to the First Edition -- Foreword to the Second Edition -- Contents -- Chapter O. Foundations -- 0.1. Topological Spaces -- 0.2. Metric Spaces -- 0.3. Linear Spaces -- 0.4. Semi-Norms -- 0.5. Locally Convex Spaces -- 0.6. The Topological Dual of a Locally Convex Space -- 0.7. Special Locally Convex Spaces -- 0.8. Banach Spaces -- 0.9. Hilbert Spaces -- 0.10. Continuous Linear Mappings in Locally Convex Spaces -- 0.11. The Normed Spaces Associated 'with a Locally Convex Space -- 0.12. Radon Measures -- Chapter 1. Summable Families -- 1.1. Summable Families of Numbers -- 1.2. Weakly Summable Families in Locally Convex Spaces -- 1.3. Summable Families in Locally Convex Spaces -- 1.4. Absolutely Summable Families in Locally Convex Spaces -- 1.5. Totally Summable Families in Locally Convex Spaces -- 1.6. Finite Dimensional Families in Locally Convex Spaces -- Chapter 2. Absolutely Summing Mappings -- 2.1. Absolutely Summing Mappings in Locally Convex Spaces -- 2.2. Absolutely Summing Mappings in Normed Spaces -- 2.3. A Characterization of Absolutely Summing Mappings in Normed Spaces -- 2.4. A Special Absolutely Summing Mappings -- 2.5. Hilbert-Schmidt Mappings -- Chapter 3. Nuclear Mappings -- 3.1. Nuclear Mappings in Normed Spaces -- 3.2. Quasinuclear Mappings in Normed Spaces -- 3.3. Products of Quasinuclear and Absolutely Summing Mappings in Normed Spaces -- 3.4. The Theorem of Dvoretzky and Rogers -- Chapter 4. Nuclear Locally Convex Spaces -- 4.1. Definition of Nuclear Locally Convex Spaces -- 4.2. Summable Families in Nuclear Locally Convex Spaces -- 4.3. The Topological Dual of Nuclear Locally Convex Spaces -- 4.4. Properties of Nuclear Locally Convex Spaces -- Chapter 5. Permanence Properties of Nuclearity -- 5.1. Subspaces and Quotient Spaces -- 5.2. Topological Products and Sums -- 5.3. Complete Hulls -- 5.4. Locally Convex Tensor Products -- 5.5. Spaces of Continuous Linear Mappings -- Chapter 6. Examples of Nuclear Locally Convex Spaces -- 6.1. Sequence Spaces -- 6.2. Spaces of Infinitely Differentiable Functions -- 6.3. Spaces of Harmonic Functions -- 6.4. Spaces of Analytic Functions -- Chapter 7. Locally Convex Tensor Products -- Introduction -- 7.1. Definition of Locally Convex Tensor Products -- 7.2. Special Locally Convex Tensor Products -- 7.3. A Characterization of Nuclear Locally Convex Spaces -- 7.4. The Kernel Theorem -- 7.5. The Complete π-Tensor Product of Normed Spaces -- Chapter 8. Operators of Type l1 and s -- 8.1. The Approximation Numbers of Continuous Linear Mappings in Normed Spaces -- 8.2. Mappings of Type P -- 8.3. The Approximation Numbers of Compact Mappings in Hilbert Spaces -- 8.4. Nuclear and Absolutely Summing Mappings -- 8.5. Mappings of Type s -- 8.6. A Characterization of Nuclear Locally Convex Spaces -- Chapter 9. Diametral and Approximative Dimension -- 9.1. The Diameter of Bounded Subsets in Normed Spaces -- 9.2. The Diametral Dimension of Locally Convex Spaces -- 9.3. The Diametral Dimension of Power Series Spaces -- 9.4. The Diametral Dimension of Nuclear Locally Convex Spaces -- 9.5. A Characterization of Dual Nuclear Locally Convex Spaces -- 9.6. The £-Entropy of Bounded Subsets in Normed Spaces -- 9.7. The Approximative Dimension of Locally Convex Spaces -- 9.8. The Approximative Dimension of Nuclear Locally Convex Spaces -- Chapter 10. Nuclear Locally Convex Spaces with Basis -- Introduction -- 10.1. Locally Convex Spaces with Basis -- 10.2. Representation of Nuclear Locally Convex Spaces with Basis -- 10.3- Bases in Special Nuclear Localty Convex Spaces -- Chapter 11. Universal Nuclear Locally Convex Spaces -- 11.1. Imbedding in the Product Space (ξ)1 -- 11.2. Embedding in the Product Space (ξ)1 -- Bibliography -- Index -- Table of Symbols

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