Abstract
Characterizations of multipliers on algebras of continuous functions with values in a commutative Banach or C*-algebra A have been obtained by several authors. In this paper, we investigate the extent to which these characterizations can be made beyond Banach algebras. We shall focus mainly on the algebras of continuous functions with values in an F-algebra A (not necessarily locally convex), in particular in a complete p-normed algebra, 0 < p <= 1, having a minimal approximate identity. We include a few examples related to our results. Most of our initial results remain valid without the commutativity of A.