A quantitative approach to disjointly non-singular operators

TL;DR

This paper introduces quantitative measures to characterize disjointly non-singular and disjointly strictly singular operators between Banach lattices and Banach spaces, providing new tools for operator analysis.

Contribution

It develops operational quantities that precisely characterize disjointly non-singular and disjointly strictly singular operators in Banach lattice settings.

Findings

Operational quantities effectively distinguish operator classes.

Characterizations apply to order continuous Banach lattices.

New tools enhance understanding of operator structure.

Abstract

We introduce and study some operational quantities which characterize the disjointly non-singular operators from a Banach lattice $E$ to a Banach space $Y$ when $E$ is order continuous, and some other quantities which characterize the disjointly strictly singular operators for arbitrary $E$.