Book:Graham R. Allan/Introduction to Banach Spaces and Algebras
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Graham R. Allan and H. Garth Dales: Introduction to Banach Spaces and Algebras
Published $\text {2011}$, Oxford University Press
- ISBN 978-0-19-920653-7
Subject Matter
Contents
- Introduction
- PART I INTRODUCTION TO BANACH SPACES
- 1. Preliminaries
- Remarks on set theory
- Metric spaces and analytic topology
- Complex analysis
- 1. Preliminaries
- 2. Elements of normed spaces
- Definitions and basic examples
- Weierstrass approximation theorems
- Inner-product spaces
- Elementary ideas on Fourier series
- Fourier integrals and Hermite functions
- 2. Elements of normed spaces
- 3. Banach spaces
- Existence of continuous linear functionals
- Separation theorems
- Category theorems
- Dual operators
- 3. Banach spaces
- PART II INTRODUCTION TO BANACH ALGEBRAS
- 4. Banach algebras
- Elementary theory
- Commutative Banach algebras
- Runge's theorem and the holomorphic functional calculus
- 4. Banach algebras
- 5. Representation theory
- Representations and modules
- Automatic continuity
- Variation of the spectral radius
- 5. Representation theory
- 6. Algebras with an involution
- Banach algebras with an involution
- $C^\ast$-algebras
- 6. Algebras with an involution
- 7. The Borel functional calculus
- The Daniell integral
- The Borel functional calculus and the spectral theorem
- 7. The Borel functional calculus
- PART III SEVERAL COMPLEX VARIABLES AND BANACH ALGEBRAS
- 8. Introduction to several complex variables
- Differentiable functions in the plane
- Functions of several complex variables
- Polynomial convexity
- 8. Introduction to several complex variables
- 9. The holomorphic functional calculus in several variables
- The main theorem
- Applications of the functional calculus
- 9. The holomorphic functional calculus in several variables
- References
- Index of terms
- Index of symbols