On the positive Dimant strongly $p$-summing multilinear operators

Abstract

In 2003, Dimant V. has defined and studied the interesting class of strongly $p$-summing multilinear operators. In this paper, we introduce and study a new class of operators between two Banach lattices, where we extend the previous notion to the positive framework, and prove, among other results, the domination, inclusion and composition theorems. As consequences, we investigate some connections between our class and other classes of operators, such as duality and linearization.

Keywords

• banach lattice
• pietsch domination theorem
• positive strongly $p$-summing multilinear operator
• positive $p$-summing operator
• tensor norm