Automatic boundedness of some operators between ordered and topological vector spaces

TL;DR

This paper investigates the conditions under which operators from ordered vector spaces to topological vector spaces are bounded and continuous, focusing on the uniform boundedness principle in this context.

Contribution

It introduces new criteria for boundedness and continuity of operators between ordered and topological vector spaces, extending the uniform boundedness principle.

Findings

Established conditions for boundedness of operators

Extended the uniform boundedness principle to ordered vector spaces

Provided new insights into the structure of such operators

Abstract

We study topological boundedness of order-to-topology bounded and order-to-topology continuous operators from ordered vector spaces to topological vector spaces. The uniform boundedness principle for such operators is investigated.