On automatic continuity of operators from ordered to topological vector spaces

TL;DR

This paper investigates conditions under which operators from ordered to topological vector spaces are automatically continuous and bounded, focusing on specific classes like Levi and Lebesgue operators.

Contribution

It provides new results on automatic continuity for operators from ordered Frechet spaces to topological vector spaces, including Levi and Lebesgue operators.

Findings

Established criteria for automatic continuity of operators

Analyzed properties of Levi and Lebesgue operators

Extended results to operators from ordered Frechet spaces

Abstract

We study continuity and boundedness of order-to-topology bounded and order-to topology continuous operators from ordered to topological vector spaces. Several results on automatic continuity of operators from ordered Frechet spaces to topological vector spaces are included. Levi and Lebesgue operators especially are investigated.