Nuclear Locally Convex Spaces / / Albrecht Pietsch.

• Superior document: Title is part of eBook package: De Gruyter DGBA Mathematics - <1990
• VerfasserIn: Pietsch, Albrecht,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2022]; ©1972
• Year of Publication: 2022
• Edition: Translated from the 2nd German Ed. by William H. Ruckle, 1969, Reprint 2021
• Language: English
• Physical Description: 1 online resource (204 p.)
• Other title: 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 --; 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
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783112564103; 9783110635881
• DOI: 10.1515/9783112564103
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Albrecht Pietsch.