Spectral Theory and Banach Algebras

Abstract

The spectrum of a bounded operator on a Banach space is best studied within the context of Banach algebras, and most of this chapter is devoted to the theory of Banach algebras. However, one should keep in mind that it is the spectral theory of operators that we want to understand. Many examples are discussed in varying detail. While the general theory is elegant and concise, it depends on its power to simplify and illuminate important examples such as those that gave it life in the first place.