Title: On the Mackey Topology of an Abelian Topological Group
by Lydia Außenhofer (Universität Passau) as part of Topological Groups
Lecture held in Elysium.
For a locally convex vector space $(V,tau)$ there exists a finest locally convex vector space topology $mu$ such that the topological dual spaces $(V,tau)’$ and $(V,mu)’$ coincide algebraically. This topology is called the $Mackey$ $topology$. If $(V,tau)$ is a metrizable locally convex vector space, then $tau$ is the Mackey topology.
In 1995 Chasco, Martín Peinador, and Tarieladze asked, “Given a locally quasi-convex group $(G,tau),$ does there exist a finest locally quasi-convex group topology $mu$ on $G$ such that the character groups $(G,tau)^wedge$ and $(G,mu)^wedge$ coincide?”
In this talk we give examples of topological groups which
1. have a Mackey topology,
2. do not have a Mackey topology,
and we characterize those abelian groups which have the property that every metrizable locally quasi-convex group topology is Mackey (i.e., the finest compatible locally quasi-convex group topology).