Locally 𝐵*-equivalent algebras

Abstract

Abstract. Let A be a Banach "-algebra. A is locally ¿"-equivalent if, for every selfadjoint element t e A, the closed *-subalgebra of A generated by / is *-isomorphic to a ¿"-algebra. In this paper it is shown that when A is locally ¿"-equivalent, and in addition every selfadjoint element in A has at most countable spectrum, then A is *-isomorphic to a ¿"-algebra.