The Norm Spectrum in Certain Classes of Commutative Banach Algebras

Abstract

Let A be a commutative Banach algebra and let Sigma(A) be its structure space. The norm spectrum sigma(f) of the functional f is an element of A* is defined by sigma(f) = ({f . a : a is an element of A}) over bar boolean AND Sigma(A), where f . a is the functional on A defined by < f . a, b > = < f, ab >, b is an element of A. We investigate basic properties of the norm spectrum in certain classes of commutative Banach algebras and present some applications.