Lattice sequence spaces and summing mappings

TL;DR

This paper develops a theoretical framework for positive summing operators in Banach lattices, characterizing various classes of these operators using sequence spaces and tensor products.

Contribution

It introduces new characterizations of positive (p; q)-summing and Cohen (p; q)-nuclear operators via sequence space analysis and tensor product continuity.

Findings

Characterization of positive strongly (p; q)-summing operators

Description of positive (p; q)-summing and Cohen (p; q)-nuclear operators

Use of tensor products to analyze operator classes

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.