Nuclear Locally Convex Spaces / / Albrecht Pietsch.
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Superior document: | Title is part of eBook package: De Gruyter DGBA Mathematics - <1990 |
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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 |
Online Access: | |
Physical Description: | 1 online resource (204 p.) |
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Table of Contents:
- 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