Multiplicative order continuous operators on Riesz algebras

TL;DR

This paper studies a class of continuous operators on Riesz algebras that respect multiplicative order convergence, introducing new operator types like mo-Lebesgue, mo-$KB$, and mo-Levi, expanding the understanding of operator behavior in this setting.

Contribution

It introduces and analyzes new classes of multiplicative order continuous operators on Riesz algebras, including mo-Lebesgue, mo-$KB$, and mo-Levi operators.

Findings

Characterization of multiplicative order continuous operators.

Introduction of mo-Lebesgue, mo-$KB$, and mo-Levi operators.

Insights into their properties and relationships.

Abstract

In this paper, we investigate operators on Riesz algebras, which are continuous with respect to multiplicative modifications of order convergence and relatively uniform convergence. We also introduce and study mo-Lebesgue, mo-$KB$, and mo-Levi operators.