Albrecht Pietsch

Nuclear Locally Convex Spaces (eBook, PDF)

• Format: PDF

Produktbeschreibung

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Produktdetails

• Verlag: De Gruyter
• Seitenzahl: 204
• Erscheinungstermin: 21. Februar 2022
• Englisch
• ISBN-13: 9783112564103
• Artikelnr.: 75336007

Inhaltsangabe

0. 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.- 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.- 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.- 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.- 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.- 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.- 6. Examples of Nuclear Locally ConvexSpaces.- 6.1. Sequence Spaces.- 6.2. Spaces of Infinitely Differentiable Functions.- 6.3. Spaces of Harmonic Functions.- 6.4. Spaces of Analytic Functions.- 7. Locally Convex Tensor Products.- 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 rc-Tensor Product of Normed Spaces.- 8. Operators of Type lp and s.- 8.1. The Approximation Numbers of Continuous Linear Mappings in Normed Spaces.- 8.2. Mappings of Type lp.- 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.- 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.- 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 Locally Convex Spaces.- 11. Universal Nuclear Locally Convex Spaces.- 11.1. Imbedding in the Product Space (?)1.- 11.2. Imbedding in the Product Space(?)1.- Table of Symbols.