Bases for Cones and Reflexivity

Abstract

It is proved that a Banach space E is non-reflexive if and only if E has a closed cone with an unbounded, closed, dentable base. If E is a Banach lattice, the same characterization holds with the extra assumption that the cone is contained in E+. This article is also a survey of the geometry (dentability) of bases for cones. Mathematics Subject Classification (1991): 46A25, 46A40, 46B10, 46B22, 46B42 Keywords: Radon-Nikodym property, dentability/unbounded convex sets, reflexivity and semi-reflexivity, ordered topological linear spaces,vector lattices, duality and reflexivity, Krein-Milman, Banach lattices, Banach, banach space, Banach lattice, lattice Quaestiones Mathematicae 24(2) 2001, 165-17