UID:
edocfu_9959240275902883
Umfang:
1 online resource (x, 794 pages) :
,
digital, PDF file(s).
ISBN:
1-139-88628-2
,
1-107-10268-5
,
1-107-08802-X
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1-107-10014-3
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1-107-09420-8
,
1-107-32577-3
Serie:
Encyclopedia of mathematics and its applications ;
Inhalt:
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 and *-algebras. This first volume is an independent, self-contained reference on Banach algebra theory. Each topic is treated in the maximum interesting generality within the framework of some class complex algebras rather than topological algebras. In both volumes proofs are presented in complete detail at a level accessible to graduate students. In addition, the books contain a wealth of historical comments, background material, examples, particularly in noncommutative harmonic analysis, and an extensive bibliography. Together these books will become the standard reference for the general theory of *-algebras.
Anmerkung:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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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
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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
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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
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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
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English
Weitere Ausg.:
ISBN 0-521-12410-7
Weitere Ausg.:
ISBN 0-521-36637-2
Sprache:
Englisch
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