Almost disjointness preservers

TL;DR

This paper investigates the stability of disjointness preservers on Banach lattices, showing that almost disjointness preserving operators can often be approximated by true disjointness preservers, but not always, with counterexamples provided.

Contribution

It provides new insights into when almost disjointness preserving operators can be approximated by disjointness preservers and highlights limitations with specific counterexamples.

Findings

Almost disjointness preserving operators are often well approximable by disjointness preservers.

There are cases where such approximation is impossible, demonstrated by counterexamples.

The study advances understanding of stability properties of operators on Banach lattices.

Abstract

We study the stability of disjointness preservers on Banach lattices. In many cases, we prove that an "almost disjointness preserving" operator is well approximable by a disjointess preserving one. However, this approximation is not always possible, as our examples show.