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Banach algebras and the general theory of *-algebras. Vol. 1, Algebras and Banach algebras /
This is the first volume of a two volume set that provides a modern account of basic Banach algebra theory including all known results on general Banach *-algebras. This account emphasises the role of *-algebra structure and explores the algebraic results which underlie the theory of Banach algebras...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
1994.
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| Colección: | Encyclopedia of mathematics and its applications ;
v. 49. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Half Title; Series Page; Title; Copyright; PREFACE; Dedication; 1 Introduction to Normed Algebras; Examples; 1.1 Norms and Semi-norms on Algebras; 1.2 Double Centralizers and Extensions; 1.3 Sums, Products and Limits; 1.4 Arens Multiplication.; 1.5 Algebras of Functions; 1.6 Matrix Algebras; 1.7 Operator Algebras; 1.8 Group Algebras on T; 1.9 Group Algebras; 1.10 Tensor Products; 2 The Spectrum; 2.1 Definition of the Spectrum; 2.2 Spectral Semi-norms; 2.3 The Jacobson Radical and the Fundamental Theorem; 2.4 Spectral Algebras; 2.5 Spectral Subalgebras and Topological Divisors of Zero
- 2.6 Numerical Range in Banach Algebras2.7 The Spectrum in Finite-Dimensional Algebras; 2.8 Spectral Theory of Operators; 2.9 Topological Algebras; 3 Commutative Algebras and Functional Calculus; 3.1 Gelfand Theory; 3.2 Silov Boundary, Hulls and Kernels; 3.3 Functional Calculus; 3.4 Examples and Applications of Functional Calculus; 3.5 Multivariable Functional Calculus; 3.6 Commutative Group Algebras; 4 Ideals, Representations and Radicals; 4.1 Ideals and Representations; 4.2 Representations and Norms; 4.3 The Jacobson Radical; 4.4 The Baer Radical; 4.5 The Brown-McCoy or Strong Radical
- 4.6 Subdirect Products4.7 Categorical Theory of Radicals; 4.8 History of Radicals and Examples; 5 Approximate Identities and Factorization; 5.1 Approximate Identities and Examples; 5.2 General Factorization Theorems; 5.3 Countable Factorization Theorems; 6 Automatic Continuity; 6.1 Automatic Continuity of Homomorphisms into A; 6.2 Automatic Continuity of Homomorphisms from A; 6.3 Jordan Homomorphisms; 6.4 Derivations; 6.5 Jordan Derivations; 7 Structure Spaces; 7.1 The Hull-Kernel Topology; 7.2 Completely Regular Algebras; 7.3 Primary Ideals and Spectral Synthesis
- 7.4 Strongly Harmonic Algebras8 Algebras with Minimal Ideals; 8.1 Finite-Dimensional Algebras; 8.2 Minimal Ideals and the Socle; 8.3 Algebras of Operators with Minimal Ideals; 8.4 Modular Annihilator Algebras; 8.5 Fredholm Theory; 8.6 Algebras with Countable Spectrum for Elements; 8.7 Classes of Algebras with Large Socle; 8.8 Examples; BIBLIOGRAPHY; INDEX; SYMBOL INDEX