The $o\tau$-continuous, Lebesgue, KB, and Levi operators between vector lattices and topological vector spaces

TL;DR

This paper explores various classes of operators between vector lattices and topological vector spaces, focusing on their continuity, boundedness, compactness, and order-related properties, with an emphasis on how topological and order structures interact.

Contribution

It introduces and analyzes operator classes like $o\tau$-continuous, Lebesgue, KB, and Levi operators, highlighting their domination properties and the interplay of topological and order structures.

Findings

Characterization of $o\tau$-continuous operators

Establishment of domination properties for operator classes

Analysis of order and topological property redistribution

Abstract

We investigate the $o\tau$-continuous/bounded/compact and Lebesgue operators from vector lattices to topological vector spaces; the KB operators between locally solid lattices and topological vector spaces; and the Levi operators from locally solid lattices to vector lattices. The main idea of operator versions of notions related to vector lattices lies in redistributing topological and order properties of a topological vector lattice between the domain and range of an operator under investigation. Domination properties for these classes of operators are studied.