Lattice sequence spaces and summing mappings (2207.11634v4)

Abstract: The objective of this study is to advance the theory concerning positive summing operators. Our focus lies in examining the space of positive strongly p-summable sequences and the space of positive unconditionally p-summable sequences. We utilize these in conjunction with the Banach lattice of positive weakly p-summable sequences to present and characterize the classes of positive strongly (p; q)-summing operators, positive (p; q)-summing, and positive Cohen (p; q)-nuclear operators. Additionally, we describe these classes in terms of the continuity of an associatedte nsor operator that is defined between tensor products of sequences spaces.