Banach Algebras and the General Theory of *-Algebras: Volume 1, Algebras and Banach Algebras

This is the first volume of a two volume set that provides a modern account of basic Banach algebra theory including all known results on general Banach *-algebras.

Theodore W. Palmer (Author)

9780521366373, Cambridge University Press

Hardback, published 25 March 1994

812 pages
24.1 x 16.3 x 4.7 cm, 1.263 kg

"The author has been very careful in researching the history of various concepts and ideas. The historical remarks in these introductions and throughout the text are a valuable addition because they show how mathematical ideas evolved... the author does an admirable job relating and ordering the various concepts...The notation is coherent and easy to follow...a valuable source for specialists and researchers..." Horst Behncke, Mathematical Reviews

This is the first volume of a two volume set that provides a modern account of basic Banach algebra theory including all known results on general Banach *-algebras. This account emphasises the role of *-algebra structure and explores the algebraic results which underlie the theory of Banach algebras and *-algebras. This first volume is an independent, self-contained reference on Banach algebra theory. Each topic is treated in the maximum interesting generality within the framework of some class complex algebras rather than topological algebras. In both volumes proofs are presented in complete detail at a level accessible to graduate students. In addition, the books contain a wealth of historical comments, background material, examples, particularly in noncommutative harmonic analysis, and an extensive bibliography. Together these books will become the standard reference for the general theory of *-algebras.

1. Introduction to normed algebras: examples
2. The spectrum
3. Commutative algebras and functional calculus
4. Ideals, representations and radicals
5. Approximate identities and factorisation
6. Automatic continuity
7. Structure spaces
8. Algebras with minimal ideals
Bibliography
Index
Symbol index.

Subject Areas: Functional analysis & transforms [PBKF]