# Topological linear spaces of formal linear sums and continuous linear operators

## TL;DR

This paper characterizes the rings of continuous linear operators on certain topological spaces of formal sums, extending to modules over ordered groups, thus advancing the understanding of operator structures in topological algebra.

## Contribution

It describes the rings of continuous linear operators on topological spaces of formal sums associated with filters and involutions, generalizing previous results to modules over ordered groups.

## Key findings

- Characterization of rings of continuous operators on formal sum spaces
- Application to modules over left ordered groups
- Extension of operator theory in topological algebra

## Abstract

The rings of linear continuous operators on the topological spaces of $\mathfrak{G}$-zero maps were described, where $\mathfrak{G}$ is a filter on a set with an involution. This applies to modules of formal series with well ordered support over left ordered groups.