Synopses & Reviews
This second volume of a two-volume set provides a modern account of basic Banach algebra theory including all known results on general Banach *-algebras. The author emphasizes the roles of *-algebra structure and explores the algebraic results that underlie the theory of Banach algebras and *-algebras. Proofs are presented in complete detail at a level accessible to graduate students. The books contain a wealth of historical comments, background material, examples, and an extensive bibliography. Together they constitute the standard reference for the general theory of *-algebras. This second volume deals with *-algebras. Noteworthy chapters develop the theory of *-algebras without additional restrictions, going well beyond what has been proved previously in this context and describe locally compact groups and the *-algebras related to them.
"This is a remarkable book...it provides the most detailed and comprehensive treatment of complex Banch*-algebras yet written...The author's writing stlye is straightforward and easy to read...Indeed, the completenedd of the exposition makes the bopok a valuable source for specialists and researchers." Mathematical Reviews
This second of two volumes gives a modern exposition of the theory of Banach algebras.
This is the second volume of a two-volume comprehensive account of basic Banach algebra theory. Proofs are presented in complete detail at a level accessible to graduate students. Both volumes contain previously unpublished results as well as examples, historical comments, and an extensive bibliography. Together they form the standard reference for the general theory of *-algebras.In this second volume, the author first develops the theory of *-algebras without additional restrictions. He proves nearly all the results previously known for Banach *-algebras and hermitian Banach *-algebras for *-algebras with algebraic restrictions and then restates these results in terms of Banach *-algebras to prove results explicitly involving the complete norm. The last chapter is devoted to locally compact groups and the related *-algebras.
Table of Contents
9. *-algebras; 10. Special *-algebras; 11. Banach *-algebras; 12. Locally compact groups and their *-algebras; Bibliography; Index; Symbol index.