Topological Algebras, Volume 185

Chapter 1: Algebraic Preliminaries

Chapter 2: Topological Preliminaries

Chapter 3: Some Type of Topological Algebras

Chapter 4: Locally Pseudo-Convex Spaces and Algebras

Chapter 5: Some Analysis

Chapter 6: Spectral Analysis in Topological Algebras

Chapter 7: Gelfand Representation Theory

Chapter 8: Commutative Topological Algebras

Chapter 9: Norm Uniqueness Theorems

Appendix. Type Chart. Biliography. Index. List of Special Symbols. List of Special Abbreviations.

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.