Book:Theo Bühler/Functional Analysis

From ProofWiki
Jump to navigation Jump to search

Theo Bühler and Dietmar A. Salamon: Functional Analysis

Published $2018$, American Mathematical Society

ISBN 978-1470441906.


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