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 *-algeb

This second of two volumes gives a modern exposition of the theory of Banach algebras.

Banach algebras are Banach spaces equipped with a continuous multipli- tion. In roughterms,there arethree types ofthem:algebrasofboundedlinear operators on Bana