Banach Algebras and the General Theory of *-Algebras: Volume 2, *-Algebras (Encyclopedia of Mathematics and its Applications) (Vol 2)

This is the second volume of a two-volume set that 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 which underlie the theory of Banach algebras and \*-algebras. Proofs are presented in complete detail at a level accessible to graduate students. The books will become the standard reference for the general theory of \*-algebras. This second volume deals with \*-algebras. Chapter 9 develops the theory of \*-algebras without additional restrictions. Chapter 10 proves nearly all the results previously known for Banach \*-algebras and hermitian Banach \*-algebras for \*-algebras with various essentially algebraic restrictions. Chapter 11 restates the previous results in terms of Banach \*-algebras and uses them to prove results explicitly involving the complete norm. Chapter 12 is devoted to locally compact groups and the \*-algebras related to them. 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 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. V. 1. Algebras And Banach Algebras -- V. 2. Algebras. Theodore W. Palmer. Includes Bibliographical References. This chapter deals with the algebraic theory of *-algebras satisfying no additional hypotheses. This second of two volumes gives a modern exposition of the theory of Banach algebras v. 1. Algebras and Banach algebras 2. [without special title].