WCOs on Non-Locally Convex Weighted Spaces of Continuous Functions

Abstract

Let CV_b(X,E) and CV₀(X,E) respectively denote the (non-locally convex) weighted spaces of continuous functions f from a completely regular Hausdorff space X into a Hausdorff topological algebra (or TVS) E for which vf(X) is bounded in E and Ï…f vanishes at infinity on X for all υ∈V, where V is a system of weights on X. In this paper, we present characterizations of weighted composition operators W_Π,T on the weighted spaces induced by scalar (or E)-valued functions on X and selfmaps T on X. Our results, in turn, generalize some recent results of Singh and Manhas (8,9,11], Singh and Singh [12] and Khan and Thaheem [2].