Copyright © 2011 Marjan Adib et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.