Quasimultipliers on \(F\)-algebras (Q535949)

Summary: 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, \(0 < k \leq 1\), 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.