Concerning dense subideals in commutative Banach algebras

Abstract

In the paper [2] we have shown that in the case of a separable Banach algebra $A$ the necessary and sufficient condition in order that a closed ideal $I\subset A$ has a dense subideal is that $I$ is not finitely (algebraically) generated. We conjectured that this result is true in the general case. In this paper we give an example showing that this conjecture fails to be true.