On the Nuclearity of Dual Groups

TL;DR

This paper proves that the dual of a locally convex nuclear $k_$ vector space with the compact-open topology is also nuclear, and extends this result to nuclear groups, establishing strong reflexivity.

Contribution

It establishes the nuclearity of dual spaces and groups in the $k_$ setting, showing strong reflexivity for nuclear $k_$-groups, which was previously unknown.

Findings

Dual of nuclear $k_$ vector space is nuclear.

Nuclear $k_$-groups are strongly reflexive.

Extension of nuclearity results from vector spaces to groups.

Abstract

We prove that the dual space of a locally convex nuclear $k_\omega$ vector space endowed with the compact--open topology is a locally convex nuclear vector space. An analogous result is shown for nuclear groups. As a consequence of this, we obtain that nuclear $k_\omega$--groups are strongly reflexive.