Book:Theo Bühler/Functional Analysis
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Theo Bühler and Dietmar A. Salamon: Functional Analysis
Published $\text {2018}$, American Mathematical Society
- ISBN 978-1470441906
Subject Matter
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