Uniform Algebras

Recently concepts from the theory of Banach algebras have been increasingly useful in applications to complex analysis. Here we give a quick survey of some, but by no means all, of these applications. The algebras which occur are algebras of complex valued functions and they are given the uniform norm with respect to some compact set K. Since the usual terms for these algebras (sup. norm algebras or function algebras) are not euphonious, we shall call them uniform algebras…