The positive Schur property on positive projective tensor products and spaces of regular multilinear operators

TL;DR

This paper characterizes the positive Schur property in positive projective tensor products of Banach lattices, linking it to the weak operator topology and providing conditions for regular multilinear operators to possess this property.

Contribution

It introduces new characterizations of the positive Schur property in tensor products and operator spaces, connecting it with topological and lattice-theoretic conditions.

Findings

Characterization of the positive Schur property in tensor products

Connection between the positive Schur property and the weak operator topology

Necessary and sufficient conditions for multilinear operators to have the positive Schur property

Abstract

We characterize the positive Schur property in the positive projective tensor products of Banach lattices, we establish the connection with the weak operator topology and we give necessary and sufficient conditions for the space of regular multilinear operators/homogeneous polynomials taking values in a Dedekind complete Banach lattice to have the positive Schur property.