Mackey’s problem – its historical background and a final solution

Lydia Außenhofer

Università di Passau

For a locally convex vector space (V,τ) there exists a finest locally convex vector space topology μ such that the topological dual spaces (V,τ)′ and (V,μ)′ coincide algebraically. This topology is called Mackey topology. If (V,τ) is a metrizable locally convex vector space, then τ is the Mackey topology. In 1995 Chasco, Mart ́ın Peinador and Tarieladze asked the following question: Given a locally quasi–convex group (G,τ), does there exist a finest locally quasi–convex group topology μ on G such that the character groups (G, τ )∧ and (G, μ)∧ coincide? In this talk we give examples of topological groups which have a Mackey topology, and we present a group which has no Mackey topology.