Commutative Banach Algebras

Abstract

Abstract In this chapter, we shall give a rather detailed description of many specific commutative Banach algebras; we shall study the examples for their own interest and for the sake of applications to automatic continuity theory in the final Chapter 5. Throughout, we shall be concerned with the basic structural properties of these examples-their character spaces, their polynomial generators, and their ideals-and we shall build up the machinery which will be required in Chapter 5.