Abstract and Applied Analysis
Volume 2004 (2004), Issue 5, Pages 387-393
doi:10.1155/S1085337504303088
A density theorem for locally convex lattices
Dimitrie Kravvaritis1
and Gavriil Păltineanu2
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
Abstract
Let E 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.