Topological algebras of locally solid vector subspaces of order bounded operators

TL;DR

This paper investigates specific subspaces of order bounded operators on a locally solid vector lattice, demonstrating that under certain conditions, these subspaces form locally solid vector lattices and complete topological algebras.

Contribution

It introduces new topologies on subspaces of order bounded operators, proving they form locally solid vector lattices and topologically complete algebras under certain conditions.

Findings

Subspaces form locally solid vector lattices

Subspaces are topologically complete algebras

Conditions for these structures are established

Abstract

Let E be a locally solid vector lattice. In this paper, we consider two particular vector subspaces of the space of all order bounded operators on E. With the aid of two appropriate topologies, we show that under some conditions, they establish both, locally solid vector lattices and topologically complete topological algebras.