http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
1 online resource (xi, 359 pages) : illustrations.
A powerful introduction to one of the most active areas of theoretical and applied mathematicsThis 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 occasionally using the more general topological vector space and locally convex space setting, it emphasizes the development of the reader's mathematical maturity and the ability to both understand and ""do"" mathematics. In so doing, Functional Analysis provides a strong springboard for further ex.
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
Includes bibliographical references (pages 341-344) and indexes.
Pure and applied mathematics (John Wiley & Sons : Unnumbered)