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-BanachTheorem
2.2 The Banach-SteinhausTheorem
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 Functionals
3.2 Dual Systems and Weak Topologies
3.3 Convergence and Compactness in Weak Topologies
3.4 The Krein-MilmanTheorem
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 Principles
6.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
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