- 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.
North-Holland Mathematics Studies
Published: November 2000
.....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
- 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.