Quasimultipliers on F -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 $F$-algebras, in particular on complete $k$-normed algebras, $0\lt k\le 1$, not necessarily locally convex. We include a few counterexamples to demonstrate that some of our results do not carry over to general $F$-algebras. The bilinearity and joint continuity of quasimultipliers on an $F$-algebra $A$ are obtained under the assumption of strong factorability. Further, we establish several properties of the strict and quasistrict topologies on the algebra $QM\left(A\right)$ of quasimultipliers of a complete $k$-normed algebra $A$ having a minimal ultra-approximate identity.