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.

Review of the hardback:‘It will become a standard reference …’

George Willis Source: Journal of London Mathematical Society

Review of the hardback:'This volume (as well as the first one) is written in a lucid, easily readable style (for graduate students). A number of examples and historical comments enlighten the abstract theoretical discussion. The volume contains a very rich 'bibliography' (on 109 pages!). This two-volume monograph is warmly recommended to graduate students and researchers interested in Banach algebras and *-algebras.'

Source: Acta. Sci. Math.

Review of the hardback:‘With a bibliography of more than 100 pages, these two volumes will form an excellent reference for the subject.’

Source: Mathematika

Review of the hardback:'It is immediately obvious that this is a mammoth work … the author has a truly remarkable knowledge of the literature, and this has been assimilated into the text.’

Source: Proceedings of the Edinburgh Mathematical Society