A characterization of regular maximal ideals

Abstract

We show that if A is generated by a single element then a closed subspace M of codimension one in A and satisfying (1) is a regular maximal ideal and we show by an example that this result may fail for an algebra which is generated two elements. We have results related to the above, which can be applied to Lι(G), where G is a locally compact abelian metrizable group; a sample corollary is that a (not a priori closed) subspace M of codimension one for which (1) holds is a regular maximal ideal in Lι(G).