A characterization of Pontryagin-van Kampen duality for locally convex spaces

Topological vector spaces (TVSs) are topological Abelian groups when considered under the operation of addition. It is therefore natural to ask when they satisfy Pontryagin-van Kampen (P-vK) duality. In 1984 S. Kye published a characterization of P-vK duality for real locally convex spaces (LCSs). His proof however is incorrect. In this paper we offer an alternative characterization of P-vK duality for real LCSs. We also compare our results with some other contributions and state a number of questions. (C) 2002 Elsevier Science B.V. All rights reserved.