Quasimultipliers on F-Algebras.

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 < k ≤ 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(A) of quasimultipliers of a complete k-normed algebra A having a minimal ultra-approximate identity. [ABSTRACT FROM AUTHOR]