Bounded orthomorphisms between locally solid vector lattices

TL;DR

This paper explores bounded orthomorphisms in locally solid vector lattices, establishing a key theorem extension and analyzing their topological and ordered structures.

Contribution

It extends the Zannen theorem to bounded orthomorphisms and investigates their topological and ordered properties.

Findings

Extended Zannen theorem to bounded orthomorphisms.

Analyzed topological structures of bounded orthomorphisms.

Studied ordered structures of these classes.

Abstract

The main aim of the present note is to consider bounded orthomorphisms between locally solid vector lattices. We establish a version of the remarkable Zannen theorem regarding equivalence between orthomomorphisms and the underlying vector lattice to the case of all bounded orthomomorphisms. Furthermore, we investigate topological and ordered structures for these classes of orthomorphisms, as well.