chapter  2
15 Pages

Banach Algebras

ByS.R. Caradus, W.E. Pfaffenberger, Bertram Yood

This chapter provides brief introduction to an idea which has considerable importance for the theory of Banach algebras. Some of the basic facts and ideas of the theory of Banach algebras are essential to linear operator's development. Of great importance for the development and applications of the subject are commutative Banach algebras of functions. The simplest nontrivial example is, perhaps, the algebra A of all continuous complex-valued functions on a locally compact Hausdorff space which 'vanish at infinity'. The algebraic operations are the pointwise operations and the norm is the sup norm. The chapter concludes with a few remarks about semisimplicity.