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Functional Analysis : an Introduction to Banach Space Theory.
A powerful introduction to one of the most active areas of theoretical and applied mathematics This distinctive introduction to one of the most far-reaching and beautiful areas of mathematics focuses on Banach spaces as the milieu in which most of the fundamental concepts are presented. While occasi...
| Clasificación: | Libro Electrónico |
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| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Wiley-Interscience
2011.
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| Colección: | Pure and applied mathematics (John Wiley & Sons : Unnumbered)
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Functional Analysis: An Introduction to Banach Space Theory; CONTENTS; Preface; Introduction; Notation and Conventions; Products and the Product Topology; Finite-Dimensional Spaces and Riesz's Lemma; The Daniell Integral; 1. Basic Definitions and Examples; 1.1 Examples of Banach Spaces; 1.2 Examples and Calculation of Dual Spaces; 2. Basic Principles with Applications; 2.1 The Hahn-Banach Theorem; 2.2 The Banach-Steinhaus Theorem; 2.3 The Open-Mapping and Closed-Graph Theorems; 2.4 Applications of the Basic Principles; 3. Weak Topologies and Applications
- 3.1 Convex Sets and Minkowski Functionals3.2 Dual Systems and Weak Topologies; 3.3 Convergence and Compactness in Weak Topologies; 3.4 The Krein-Milman Theorem; 4. Operators on Banach Spaces; 4.1 Preliminary Facts and Linear Projections; 4.2 Adjoint Operators; 4.3 Weakly Compact Operators; 4.4 Compact Operators; 4.5 The Riesz-Schauder Theory; 4.6 Strictly Singular and Strictly Cosingular Operators; 4.7 Reflexivity and Factoring Weakly Compact Operators; 5. Bases in Banach Spaces; 5.1 Introductory Concepts; 5.2 Bases in Some Special Spaces; 5.3 Equivalent Bases and Complemented Subspaces
- 5.4 Basic Selection Principles6. Sequences Series and a Little Geometry in Banach Spaces; 6.1 Phillips' Lemma; 6.2 Special Bases and Reflexivity in Banach Spaces; 6.3 Unconditionally Converging and Dunford-Pettis Operators; 6.4 Support Functionals and Convex Sets; 6.5 Convexity and the Differentiability of Norms; Bibliography; Author/Name Index; Subject Index; Symbol Index