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

[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.J.M. Calabuig and O. Blasco were supported by Ministerio de Economia y Competitividad (Spain) (project MTM2011-23164). E.A. Sanchez-Perez was supported by Ministerio de Economia y Competitividad (Spain) (project MTM2012-36740-C02-02).Blasco De La Cruz, O.; Calabuig, JM.; Sánchez Pérez, EA. (2015). p-Variations of vector measures with respect to vector measures and integral representation of operators. Banach Journal of Mathematical Analysis. 9(1):273-285. doi:10.15352/bjma/09-1-20S2732859