A class of operators from a Banach lattice into a Banach space (Q1089601)

The paper is devoted to studying the class of operators from a Banach lattice X into a Banach space B which map positive X-valued sequences in \(weak-\ell^ p\) into B-valued sequences in \(\ell^ q\). These classes are related to (p,q)-absolutely summing operators considered by Pietsch and operators of type \(\leq (p,q)\) defined by Maurey. We obtain several characterizations of these operators, and consider the special case \(X=\ell^ r\). We finally related them to the Orlicz property on Banach lattices.