Accessible Prime Ideals in Commutative Banach Algebras

Abstract

A non-maximal closed prime ideal P in a commutative unital Banach algebra B is said to be accessible if P equals to the intersection of all closed ideals of B properly containing it. In this paper it is shown that a non-maximal closed prime ideal P is accessible if there exists a sequence {I_n} of ideals properly containing P is such that ∩I_n=P. Some non-trivial examples of accessible prime ideals are given.