Lydia Außenhofer - ATTI 2026 | Algebra, Topology and Their Interactions

On the Mackey topology on abelian topological groups

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 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 the following question: 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 case such a topology exists, it is called the Mackey topology for $(G,\tau)$ .
In this talk we give examples of topological groups which
– have a Mackey topology,
– do not have a Mackey topology,
and we characterize in the class of bounded abelian groups all locally quasi-convex group topologies which are Mackey.

M	T	W	T	F	S	S
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17	18	19	20	21	22	23
24	25	26	27	28	29	30
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