MOSCO CONVERGENCE AND WEAK TOPOLOGIES FOR CONVEX-SETS AND FUNCTIONS

Let X be a reflexive Banach space. This article presents a number of new characterizations of the topology of Mosco covergence tau-M for convex sets and functions in terms of natural geometric operators and functionals. In addition, necessary and sufficient conditions are given for tau-M to agree with the weak topology generated by {d(x, C): x is-an-element-of X}, where each distance functional is viewed as a function of the set argument.