OPERATORS AND DYNAMICAL-SYSTEMS ON WEIGHTED FUNCTION-SPACES

Let X be a completely regular Hausdorff space, let V be a system of we ights on X and let E be a locally convex Hausdorff space. Let CV0(X, E ) and CVb(X, E) be the weighted locally convex spaces of vector-valued continuous functions with a topology generated by seminorms which are weighted analogue of the supremum norm. In the present paper, we char acterize multiplication operators and weighted composition operators o n the spaces CV0(X, E) and CVb(X, E) induced by scalar-valued and vect or-valued mappings. A (linear) dynamical system on these weighted spac es is obtained as an application of the theory of multiplication opera tors.