A Class of Complete Metrizable A-Module Pairings

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Science, University of Payame Noor (PNU), Tehran, Iran

2 Department of Basic Sciences, Faculty of Basic Science, Technical and Vocational University (TVU), Tehran, Iran

10.22091/maa.2026.17152.1065

Abstract

In this paper, a new class of topological $A$-module pairings is introduced and studied. This class is based on complete metrizable topological vector spaces possessing a countable fundamental system of bounded sets. It is shown that, within this framework, the set of all continuous linear operators admitting adjoints with respect to the pairing forms a complete metrizable topological algebra. We also investigate the relationship between this structure and locally bounded algebras, and provide examples of dually irreducible pairings. These results naturally extend the classical theory of Bonsall--Duncan for Banach $A$-module pairings and provide a suitable framework for further developments in the theory of topological algebras and their modules.

Keywords

Main Subjects

Measure Algebras and Applications

Articles in Press, Accepted Manuscript
Available Online from 29 September 2026

Files

Share

How to cite

Statistics