On reflexive groups and function spaces with a Mackey group topology

TL;DR

This paper establishes conditions under which reflexive abelian groups and certain function spaces are Mackey groups, linking dual properties and topological features.

Contribution

It proves that reflexive abelian groups with specific dual properties are Mackey groups and characterizes when function spaces are barrelled or Mackey groups.

Findings

Reflexive abelian groups with duals having the qc-Glicksberg property are Mackey groups.

Reflexive abelian groups of finite exponent are Mackey groups.

For a realcompact space, the space C_k(X) is barrelled if and only if it is a Mackey group.

Abstract

We prove that every reflexive abelian group $G$ such that its dual group $G^\wedge$ has the $qc$-Glicksberg property is a Mackey group. We show that a reflexive abelian group of finite exponent is a Mackey group. We prove that, for a realcompact space $X$, the space $C_k(X)$ is barrelled if and only if it is a Mackey group.