Finite codimensional ideals in Banach algebras

Abstract

ABSTRACT. Let A be a commutative, selfadjoint, point spectral Banach algebra and let M be a finite codimensional closed subspace of A such that for each f in M there are n distinct maximal ideals l[,... ,rn of A with / € //. We prove that then there are distinct maximal ideals I\, ■ ■., In of A such that M C Ii Pi • • • Pi In', in particular if codim(M) = n, then M is an ideal.