Points of Weak^* - norm continuity in the unit ball of the space WC(K,X)^*

Abstract

For a compact Hausdorff space with a dense set of isolated points, we give a complete description of points of weak^* -norm continuity in the dual unit ball of the space of Banach space valued functions that are continuous when the range has the weak topology. As an application we give a complete description of points of weak-norm continuity of the unit ball of the space of vector measures when the underlying Banach space has the Radon-Nikodym property.