WEAKLY COMPACT LINEAR OPERATORS ON WEIGHTED SPACES OF CONTINUOUS FUNCTIONS

ABSTRACT. Let V be a Nachbin family of upper semicontinuous functions on a locally compact Hausdorff space X, and let CV0(X) denote the corresponding weighted space of continuous functions. The main result in this paper is a vector measure representation of weakly compact linear operators with domain CV0(X) and range in a locally convex space. Section 1. Introduction and preliminarie