Pontryagin duality for topological Abelian groups
by
Salvador Hernández
Universitat Jaume I

A topological abelian group G satisfies Pontryagin duality, or is Pontryagin reflexive for short, if the natural homomorphism of G to its bidual group is a topological isomorphism. The aim of this talk is to report on some recent results related to Pontryagin duality theory of topological Abelian groups. In particular, we look at the question, set by Kaplan in 1948, of characterizing the topological Abelian groups for which Pontryagin duality holds (Pontryagin reflexive groups). We present a solution to this question using the notion of "groups in duality" introduced by Varopoulos in 1964. An example is also given to correct a wrong statement appearing in previously existent characterizations of Pontryagin reflexive groups.

Paper reference: atlas:vaaa-92

Date received: August 29, 2000