Pontryagin duality for topological abelian groups
by
Salvador Hernandez
Universidad Jaume I, departamento de Matematicas, 12071-Castellon (Spain)

A topological abelian group G is Pontryagin reflexive, or P-reflexive for short, if the natural homomorphism of G to its bidual group is a topological isomorphism. In this talk we look at the question, set by Kaplan in 1948, of characterizing the topological Abelian groups that are P-reflexive. Thus, we find some conditions on an arbitrary group G that are equivalent to the P-reflexivity of G and give an example that corrects a wrong statement appearing in previously existent characterizations of P-reflexive groups. Some other related properties of topological Abelian groups are also considered.

Date received: January 24, 2000