p-Variations of vector measures with respect to vector measures and integral representation of operators

Abstract

[EN] In this paper we provide two representation theorems for two relevant classes of operators from any p-convex order continuous Banach lattice with weak unit into a Banach space: the class of continuous operators and the class of cone absolutely summing operators. We prove that they can be characterized as spaces of vector measures with finite p-semivariation and p-variation, respectively, with respect to a fixed vector measure. We give in this way a technique for representing operators as integrals with respect to vector measures.