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Cone characterization of reflexive Banach lattices

Published online by Cambridge University Press:  18 May 2009

Ioannis A. Polyrakis
Ioannis A. Polyrakis
Affiliation:
Department of Mathematics, National Technical University, Zografou Campus 15780 Athens, Greece e-mail: ypoly@hisyros.ntua.gr
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Abstract

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We prove that a Banach lattice X is reflexive if and only if X+ does not contain a closed normal cone with an unbounded closed dentable base.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 1 , January 1995 , pp. 65 - 67
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

REFERENCES

1.Aliprantis, C. D. and Burkinshaw, O., Positive operators (Academic Press, 1985).Google Scholar
2.Diestel, J. and Uhl, J. J., Vector measures (Math. Surveys, Vol. 15. Amer. Math. Soc., 1977).CrossRefGoogle Scholar
3.Jameson, G. J. O., Ordered linear spaces, Lecture Notes in Mathematics No 141 (Springer-Verlag, 1970).CrossRefGoogle Scholar
4.Lozanovskñ, G. Ya., Banach structures and bases, Functional Analysis and its Applictions 1 (1967), 249.CrossRefGoogle Scholar
5.Polyrakis, I. A., Extreme points of unbounded, closed and convex sets in Banach spaces, Math. Proc. Cambridge Phil. Soc. 95 (1984), 319–323.CrossRefGoogle Scholar
6.Polyrakis, I. A., Cones locally isomorphic to the positive cone of l1(Γ), Linear Algebra and Appl. 84 (1986), 323–334.CrossRefGoogle Scholar
7.Singer, I., Bases in Banach spaces I (Springer-Verlag, 1974).Google Scholar