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, 165-173