UID:
almahu_9947367694302882
Format:
1 online resource (459 p.)
ISBN:
1-281-03878-4
,
9786611038786
,
0-08-054308-1
Series Statement:
North-Holland mathematics studies, 185
Content:
This book consists of nine chapters. Chapter 1 is devoted to algebraic preliminaries. Chapter 2 deals with some of the basic definition and results concerning topological groups, topological linear spaces and topological algebras. Chapter 3 considered some generalizations of the norm. Chapter 4 is concerned with a generalization of the notion of convexity called p-convexity. In Chapter 5 some differential and integral analysis involving vector valued functions is developed. Chapter 6 is concerned with spectral analysis and applications. The Gelfand representation theory is the subject-mat
Note:
Originally published: New Delhi : Narosa Pub. House, 1999.
,
Front Cover; Topological Algebras; Copyright Page; Contents; Preface; Chapter 1. Algebraic Preliminaries; 1. Some Basic Concepts and Results; 2. Ideals and Radical; 3. Characters and Hypermaximal Ideals; 4. Extensions of Ideals; 5. Regular Representation and Primitive Ideal; 6. Real and Complex Algebras; 7. Spectrum and Quasi-spectrum; 8. Extended Spectrum and Extended Quasi-spectrum; 9. Strictly Real Algebras; Chapter 2. Topological Preliminaries; 1. Topological Groups and Linear Spaces; 2. Topological Algebras
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3. Completions of Topological Linear Spaces and Topological AlgebrasChapter 3. Some Types of Topological Algebras; 1. Quarter-norms; 2. ρ-Seminorms; 3. Quarternormed Algebras.(F) Algebras; 4. ρ-Seminormed Algebras; ρ-Banach Algebras; 5. Bounded Linear Transformations on ρ -Seminormed Linear Spaces; 6. Topological Algebras with Inverses; 7. Topological Zero Divisors; Chapter 4. Locally Pseudo-Convex Spaces and Algebras; 1. ρ-Convexity; 2. Locally Bounded Algebras; 3. Locally Pseudo-Convex Spaces; 4. Locally Pseudo-Convex Algebras; 5. Projective Limit Decomposition
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6. Metrizable Locally Pseudo-Convex Algebras 7. Ample Algebras; 8. Topological Spectral Radius; Chapter 5. Some Analysis; 1. Vector-valued Differentiability and Analyticity; 2. Exponential and Logarithmic Vector Functions; 3. Square Roots and Quasi-square Roots; 4. Complex Vector-valued Line Integrals and Cauchy's Theorems; 5. Power Series Operations in Topological Algebras; Chapter 6. Spectral Analysis in Topological Algebras; 1. Spectral Properties; 2. The Resolvent Function; 3. The Pseudo-Resolvent Function; 4. Spectral Algebras
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5. Gelfand-Mazur and Other Similar Theorems 6. Turpin's Theorem on Locally Convex Algebras; Chapter 7. Gelfand Representation Theory; 1. Ideals of Topological Algebras; 2. Gelfand Algebras; 3. The Gelfand Representation; 4. GB Algebras; 5. Holomorphic Functional Calculus for a Single Algebra Element; 6. Automorphisms and Derivations; Chapter 8. Commutative Topological Algebras; 1. Function Algebras; 2. Shilov Boundary; 3. Hull-Kernel Topology; 4. Completely Regular Algebras; 5. Holomorphic Functional Calculus for Several Commutative Algebra Elements
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6. Shilov Idempotent TheoremChapter 9. Norm Uniqueness Theorems; 1. Norm-uniqueness Theorem of Gelfand; 2. Rickart Seperating Function; 3. Topological Modules; 4. Norm-Uniqueness Theorems for Non-commutative Algebras; Appendix; Type Chart; Bibliography; Index; List of Special Symbols; List of Special Abbreviations
,
English
Additional Edition:
ISBN 0-444-50609-8
Language:
English
