Generalized Local Operators Between Function Modules

Abstract

Let X be a compact Hausdorff space, E be a normed space, A(X,E) be a regular Banach function algebra on X , and A(X,E) be a subspace of C(X,E) . In this paper, first we introduce the notion of localness of an additive map S:A(X,E) → C(X,E) with respect to additive maps T1,...,Tn: A(X) → C(X) and then we characterize the general form of such maps for a certain class of subspaces A(X,E) of C(X,E) having A(X)-module structure. ./files/site1/files/71/9.pdf

Keywords

• local operator
• separating map
• lipschitz functions
• absolutely continuous functions
• vector-valued continuous functions