RT Journal Article
T1 Completeness properties of locally quasi-convex groups
A1 Bruguera Padró, M. Montserrat
A1 Chasco, M.J.
A1 Martín Peinador, Elena
A1 Tarieladze, Vaja
AB It is natural to extend the Grothendieck theorem on completeness, valid for locally convex topological vector spaces, to Abelian topological groups. The adequate framework to do it seems to be the class of locally quasi-convex groups. However, in this paper we present examples of metrizable locally quasi-convex groups for which the analogue to the Grothendieck theorem does not hold. By means of the continuous convergence structure on the dual of a topological group, we also state some weaker forms of the Grothendieck theorem valid for the class of locally quasi-convex groups. Finally, we prove that for the smaller class of nuclear groups, BB-reflexivity is equivalent to completeness. (C) 2001 Elsevier Science B.V.
PB Elsevier Science
SN 0166-8641
YR 2000
FD 2000-04-16
LK https://hdl.handle.net/20.500.14352/57583
UL https://hdl.handle.net/20.500.14352/57583
LA eng
NO International School of Mathematics G Stampacchia 27th Course: Convergence and Topology.JUN 27-JUL 02, 1998.ERICE, ITALY
DS Docta Complutense
RD 20 abr 2025