Topological algebras of statistical $\tau$-bounded operators on ordered topological vector spaces

TL;DR

This paper introduces statistical bounded sets and explores classes of bounded operators on topological vector spaces, analyzing their algebraic properties and relations to order bounded operators within the context of ordered topological vector spaces.

Contribution

It defines statistical bounded sets and studies three classes of bounded operators, establishing their relations and algebraic properties in ordered topological vector spaces.

Findings

Defined statistical bounded sets on topological vector spaces

Established relations between classes of bounded operators and order bounded operators

Analyzed algebraic properties of these operators under uniform convergence topology

Abstract

In this paper, we introduce statistical bounded set on topological vector space. Also, we consider three classes of bounded operators from topological vector spaces to ordered topological vector spaces. Moreover, we give relations between them and order bounded operators. We give algebraic properties of these operators concerning to the uniform convergence topology.