Nuclear Locally Convex Spaces / Albrecht Pietsch.

Format:

Book

Author/Creator:

Pietsch, A. (Albrecht), Author.

Language:

English

Subjects (All):

Locally convex spaces.

Linear topological spaces.

Physical Description:

1 online resource (204 p.)

Edition:

Translated from the 2nd German Ed. by William H. Ruckle, 1969, Reprint 2021

Place of Publication:

Berlin ; Boston : De Gruyter, [2022]

Language Note:

In English.

Summary:

No detailed description available for "Nuclear Locally Convex Spaces".

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

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

Notes:

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 02. Mrz 2022)

Description based on publisher supplied metadata and other sources.

ISBN:

3-11-256410-3

OCLC:

1301550175