Quasimultipliers on -Algebras

Abstract

We investigate the extent to which the study of quasimultipliers can be made beyond Banach algebras. We will focus mainly on the class of -algebras, in particular on complete -normed algebras, , not necessarily locally convex. We include a few counterexamples to demonstrate that some of our results do not carry over to general -algebras. The bilinearity and joint continuity of quasimultipliers on an -algebra are obtained under the assumption of strong factorability. Further, we establish several properties of the strict and quasistrict topologies on the algebra of quasimultipliers of a complete -normed algebra having a minimal ultra-approximate identity.