FACIAL STRUCTURE OF CONVEX SETS IN BANACH SPACES AND INTEGRAND REPRESENTATION OF CONVEX OPERATORS

Abstract

Many types of convex operators which take values in some complete lattices can be represented by convex integrands. We consider a certain structure of faces of convex sets, and give a new proof of the representation theorem which is applicable in infinite-dimensional cases. As an application of such representations, we consider the conjugate duality of convex operators.