Functional Analysis (Pure and Applied Mathematics, Vol. 81)

✍ Scribed by Carl DeVito

• Publisher: Academic Press
• Year: 1978
• Tongue: English
• Leaves: 177
• Edition: 0
• Category: Library

✦ Table of Contents

Functional Analysis
Copyright Page
Contents
Preface
Chapter 1. Preliminaries
1. Norms on a Vector Space
2. Finite Dimensional Normed Spaces
3. Infinite Dimensional Spaces. Hamel and Schauder Bases
Chapter 2. Operator Theory
1. Compact Linear Operators
2. Riesz Theory and Complementary Subspaces
3. The Open-Mapping Theorem
4. Quotient Spaces of l1
5. The Closed Graph Theorem
Chapter 3. Linear Functionals
1. Special Subspaces of Ia and l1. The Dual Space
2. The Hahn–Banach Theorem
3. The Banach–Steinhaus Theorem
4. The Completion of a Normed Space. Reflexive Banach Spaces
Chapter 4. The Weak Topology
1. Topology from a Family of Seminorms
2. Sets Which Define Seminorms
3. Locally Convex Spaces. Kolmogorov's Theorem
4. The Hahn–Banach Theorem. Reflexive Banach Spaces
Chapter 5. More about Weak Topologies
1. Dual Spaces and the Krien–Milman Theorem
2. The Eberlein–Smulian Theorem
Chapter 6. Applications to Analysis
1. Applications to Trigonometric Series
2. Miscellaneous Applications
Chapter 7. The Theory of Distributions
1. Some Function Spaces. Partitions of Unity
2. Fréchet Spaces
3. The Fourier Transform
4. Distributions: Definition and Characterizations
5. Distributions: Examples. Properties, and Applications
Appendix A: Solutions to Starred Problems in Chapters 1–4
Appendix B: Reflexive Banach Spaces
References
Index