UID:
almahu_9947366347402882
Format:
1 online resource (177 p.)
ISBN:
1-281-76333-0
,
9786611763336
,
0-08-087397-9
Series Statement:
Pure and applied mathematics, a series of monographs and textbooks ; 81
Content:
Functional analysis
Note:
Includes index.
,
Front Cover; 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 SpacesChapter 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 Transform4. 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
,
English
Additional Edition:
ISBN 0-12-213250-5
Language:
English
