When is the range of a multiplier on a Banach algebra closed?

Abstract

In this paper we prove the Theorem: Let A be a Banach algebra with a bounded approximate identity (=BAI) such that every proper closed ideal of A is contained in a proper closed ideal with a BAI. Then a multiplier T : A -> A has a closed range iff T factors as a product of an idempotent multiplier and an invertible multiplier.