Multiplication Operators on Weighted Spaces of Vector-Valued Continuous Functions

If V is a system of weights on a completely regular Hausdorff space X and E is a locally convex space, then CV_Q(X, E) and CV_b(X, E) are locally convex spaces of vector-valued continuous functions with topologies generated by seminorms which are weighted analogues of the supremum norm. In this paper we characterise multiplication operators on these spaces induced by scalar-valued and vector-valued mappings. Many examples are presented to illustrate the theory.