Maurey-Rosenthal factorization for \(p\)-summing operators and Dodds-Fremlin domination (Q2919623)

The authors 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, they 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. They also present a new characterization of Banach lattices satisfying a lower 2-estimate in terms of the order properties of 2-summing operators.