An extension of the Krein-Smulian and Lozanovskii theorems to metrizable spaces with a cone

Abstract

The Krein-Smulian theorem that a closed generating cone in a Banach space is nonflattened and a theorem of Lozanovskii about the automatic continuity of linear positive operators are generalized to completely metrizable topological vector spaces. © 2011 Pleiades Publishing, Ltd.