Weakly compact operators on \(C_ 0(S,A)\) (Q1062258)

The principal aim of this paper is to provide a survey of some of the existing results concerning weakly compact operators on continuous function spaces. Let A, B be locally convex Hausdorff topological vector spaces, S be a topological space. The space of all continuous functions from S to A vanishing at infinity is denoted by \(C_ 0(S,A)\). A Riesz type representation theorem for bounded linear operators T:\(C_ 0(S,A)\to B\) is considered for the case where S is locally compact. Convolution of vector-measures is also considered. The last section of the paper is devoted to the case where S is completely regular.