Almost Disjointness Preservers

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 disjointness preserving one. However, this approximation is not always possible, as our examples show.

Invertible disjointness preserving operators

It is shown that an invertible disjointness preserving operator from a uniformly complete vector lattice onto a normed vector lattice has a disjointness preserving inverse and is necessarily order bounded.