Lattice sequence spaces and summing mappings

Abstract

The aim of this work is to contribute to the theory of positive summing operators, we focus on the space of positive strongly p-summable sequences and the space of positive uncondutionaly p-summable sequences, we use it together with the space of positive weakly p-summable sequences to define some classes of positive summing operatorsto and characterize the classes of positive strongly (p, q)-summing operators, positive (p, q)-summing, and the positive (p, q)-nuclear operators. Also, we prove that, the class of positive strongly p-summing is the class of p-majorizing operators.