Abstract. Let $X$ be a completely regular Hausdorff space and let $E$ be a locally convex Hausdorff space. If $V$ is a system of weights, then $CV_o(X,E)$ and $CV_p(X,E)$ are weighted spaces of continuous functions with topologies derived from seminorms which are weighted analogues of the supremum norm. We characterize the self-maps of the underlying space $X$ which induce composition operators on these weighted spaces and then give a characterization of linear transformations which are composition operators on weighted spaces. Some properties of these composition operators on weighted spaces are given. Most of the results of [Si-Su2] are obtained as an application of the results of this paper.

AMS Subject Classification (1991): 47B38, 46E40

Keyword(s): weighted space, composition operators

Received October 1, 1992. (Registered under 5561/2009.)