On composition operators between weighted (LF)‐ and (PLB)‐spaces of continuous functions

Abstract

AbstractLet X be a locally compact Hausdorff topological space, let be a system of positive continuous functions on X and let φ be a continuous self‐map on X. The composition operators on the weighted function (LF)‐spaces (, resp.) and on the weighted function (PLB)‐spaces (, resp.) are studied. We characterize when the operator acts continuously on such spaces in terms of the system and the map φ, as well as we determine conditions on and φ which correspond to various basic properties of the composition operator , like boundedness, compactness, and weak compactness. Our approach requires a study of the continuity, boundedness, (weak) compactness of the linear operators between (LF)‐spaces and (PLB)‐spaces.