Topological Algebras


  • V.K. Balachandran, Ramanujan Institute for Advanced Studies in Mathematics, Chennai, India.

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.
View full description


Book information

  • Published: November 2000
  • Imprint: NORTH-HOLLAND
  • ISBN: 978-0-444-50609-2


.....the book is readable, concise, clear and well-organized. It is self-contained, including detailed, but not jumbly, discussions on basic aspects of the theory such as inversion or relationships between the real and complex case.......
J.E. Galé, Mathematical Reviews

Table of Contents

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.