Book:Gert K. Pedersen/Analysis Now/Second Edition

Subject Matter

 * Functional Analysis

Contents
Preface


 * Chapter 1: General Topology


 * 1.1 Ordered Sets
 * 1.2 Topology
 * 1.3 Convergence
 * 1.4 Continuity
 * 1.5 Separation
 * 1.6 Compactness
 * 1.7 Local Compactness


 * Chapter 2: Banach Spaces


 * 2.1 Normed Spaces
 * 2.2 Category
 * 2.3 Dual Spaces
 * 2.4 Seminormed Spaces
 * 2.5 $w^*$-compactness


 * Chapter 3: Hilbert Spaces
 * 3.1 Inner products
 * 3.2 Operators on Hilbert Space
 * 3.3 Compact Operators
 * 3.4 The Trace


 * Chapter 4: Spectral Theory


 * 4.1 Banach Algebras
 * 4.2 The Gelfand Transform
 * 4.3 Function Algebras
 * 4.4 The Spectral Theorem, I
 * 4.5 The Spectral Theorem, II
 * 4.6 Operator Algebra
 * 4.7 Maximal Commutative Algebras


 * Chapter 5: Unbounded Operators


 * 5.1 Domains, Extensions and Graphs
 * 5.2 The Cayley Transform
 * 5.3 Unlimited Spectral Theory


 * Chapter 6: Integration Theory


 * 6.1 Radon Integrals
 * 6.2 Measurability
 * 6.3 Measures
 * 6.4 $L^p$ spaces
 * 6.5 Duality theory
 * 6.6 Product Intergrals

Bibliography

List of Symbols

Index