Maurey-Rosenthal factorization for p-summing operators and Dodds-Fremlin domination

Abstract

We characterize by means of a vector norm inequality the space of operators that factorize through a p-summing operator from an L-r-space to an L-s-space. As an application, we prove a domination result in the sense of Dodds-Fremlin for p-summing operators on Banach lattices with cotype 2, showing moreover that this cannot hold in general for spaces with higher cotype. We also present a new characterization of Banach lattices satisfying a lower 2-estimate in terms of the order properties of 2-summing operators.