Multiplication operators on weighted spaces of vector-valued continuous functions

Abstract

Abstract If V is a system of weights on a completely regular Hausdorff space X and E is alocally convex space, then CV 0 ( 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.