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

ISBN-13: 9780521366373 / Angielski / Twarda / 1994 / 812 str.

Theodore W. Palmer (University of Oregon)

Opis

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 emphasizes the role of *-algebraic structure and explores the algebraic results that underlie the theory of Banach algebras and *-algebras. The first volume, which contains previously unpublished results, is an independent, self-contained reference on Banach algebra theory.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 of complex algebras rather than topological algebras. Proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, particularly in noncommutative harmonic analysis, and an extensive bibliography. Volume II is forthcoming.

Recenzje

"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

Spis treści

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.