Abstract and Applied Analysis
Volume 2004 (2004), Issue 5, Pages 387-393
A density theorem for locally convex lattices
1Department of Mathematics, National Technical University of Athens, Zografou Campus, Zografou 15780, Greece
2Department of Mathematics, Technical University of Civil Engineering of Bucharest, Lacul Tei Blvd.124, Sector 2, Bucharest 38 RO-020396, Romania
Received 16 October 2002
Copyright © 2004 Dimitrie Kravvaritis and Gavriil Păltineanu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a real, locally convex, locally solid vector lattice of
(AM)-type. First, we prove an approximation theorem of
Bishop's type for a vector subspace of such a lattice. Second,
using this theorem, we obtain a generalization of Nachbin's
density theorem for weightedspaces.