Original Articles

BASES FOR CONES AND REFLEXIVITY

Published in: Quaestiones Mathematicae
Volume 24 , issue 2 , 2001 , pages: 165–173

DOI: 10.1080/16073606.2001.9639204

Author(s): Ioannis Polyrakis Department of Mathematics, National Technical University of Athens, Zographou, Athens, Greece,

Keywords: Radon-Nikodym property , dentability , unbounded convex sets

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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.

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