Book:Theo Bühler/Functional Analysis

Subject Matter

 * Functional Analysis

Contents
Preface

Introduction


 * Chapter 1. Foundations


 * 1.1 Metric Spaces and Compact Sets


 * 1.2 Finite-Dimensional Banach Spaces


 * 1.3 The Dual Space


 * 1.4 Hilbert Spaces


 * 1.5 Banach Algebras


 * 1.6 The Baire Category Theorem


 * 1.7 Problems


 * Chapter 2. Principles of Functional Analysis


 * 2.1 Uniform Boundedness


 * 2.2 Open Mappings and Closed Graphs


 * 2.3 Hahn-Banach and Convexity


 * 2.4 Reflexive Banach Spaces


 * 2.5 Problems


 * Chapter 3. The Weak and Weak* Topologies


 * 3.1 Topological Vector Spaces


 * 3.2 The Banach-Alaoglu Theorem


 * 3.3 The Banach-Dieudonné Theorem


 * 3.4 The Eberlein-Šmulyan Theorem


 * 3.5 The Kreĭn-Milman Theorem


 * 3.6 Ergodic Theory


 * 3.7 Problems


 * Chapter 4. Fredholm Theory


 * 4.1 The Dual Operator
 * 4.2 Compact Operators
 * 4.3 Fredholm Operators
 * 4.4 Composition and Stability
 * 4.5 Problems


 * Chapter 5. Spectral Theory


 * 5.1 Complex Banach Spaces
 * 5.2 Spectrum
 * 5.3 Operators on Hilbert Spaces
 * 5.4 Functional Calculus for Self-Adjoint Operators
 * 5.5 Gelfand Spectrum and Normal Operators
 * 5.6 Spectral Measures
 * 5.7 Cyclis Vectors
 * 5.8 Problems


 * Chapter 6. Unbounded Operators


 * 6.1 Unbounded Operators on Banach Spaces


 * 6.2 The Dual of an Unbounded Operator


 * 6.3 Unbounded Operators


 * 6.4 Functional Calculus and Spectral Measures


 * 6.5 Problems


 * Chapter 7. Semigroups of Operators


 * 7.1 Strongly Continuous Semigroups


 * 7.2 The Hille-Yosida-Phillips Theorem


 * 7.3 The Dual Semigroup


 * 7.4 Analytic Semigroups


 * 7.5 Banach Space Valued Measurable Functions


 * 7.6 Inhomogeneous Equations


 * 7.7 Problems


 * Appendix A. Zorn and Tychonoff


 * A.1 The Lemma of Zorn


 * A.2 Tychonoff's Theorem

Bibliography

Notation

Index