Nuclear Locally Convex Spaces /

Nuclear Locally Convex Spaces / / Albrecht Pietsch.

Saved in:
Bibliographic Details
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
Online Access:
Physical Description:1 online resource (204 p.)
Tags: Add Tag
No Tags, Be the first to tag this record!
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

Similar Items