Topological Algebras

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Elsevier, Nov 23, 2000 - Mathematics - 460 pages
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-matter of Chapter 7. Chapter 8 deals with commutative topological algebras. Finally in Chapter 9 an exposition of the norm uniqueness theorems of Gelfand and Johnson (extended to p-Banach algebras) is given.
 

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Contents

Chapter 1 Algebraic Preliminaries
1
Chapter 2 Topological Preliminaries
73
Chapter 3 Some Types of Topological Algebras
100
Chapter 4 Locally PseudoConvex Spaces and Algebras
174
Chapter 5 Some Analysis
222
Chapter 6 Spectral Analysis in Topological Algebras
262
Chapter 7 Gelfand Representation Theory
296
Chapter 8 Commutative Topological Algebras
353
Chapter 9 Norm Uniqueness Theorems
411
Appendix
427
Type Chart
429
Bibliography
431
Index
435
List of Special Symbols
443
List of Special Abbreviations
445
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