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Lattice Banach spaces, order-isomorphic to l1

Published online by Cambridge University Press:  24 October 2008

Ioannis A. Polyrakis
Ioannis A. Polyrakis
Affiliation:
Department of Mathematics, National Technical University of Athens, Patision 42, Greece
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Extract

It is known, (see [7], theorem 4 or [8], corollary II, 10.1), that a positive generated, ordered Banach space X is order-isomorphic to l1 iff X has a Schauder basis which generates its positive cone X+ and X+ has a bounded base.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 3 , November 1983 , pp. 519 - 522
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

[1] Bourain, J. and Talagrand, M.. Dans un espace de Banach reticulé solide, la propriété de Radon-Nikodým et celle de Krein-Milman sont équivalentes. Proc. Amer. Math,. Soc. 81 (1981), 93–96.Google Scholar
[2] Diestel, J. and Uhl, J. J.. Vector Meaaurea (American Mathematical Society Surveys, 1977).Google Scholar
[3] Jameson, G. J. O.. Ordered Linear Spaces. Lecture Notes in Math. vol. 141 (Springer-Verlag, 1970).CrossRefGoogle Scholar
[4] Kendall, D.. Simplexes and vector lattices. J. London Math. Soc. 37 (1962), 365–371.CrossRefGoogle Scholar
[5] Lindenstrauss, J.. On extreme points of l l. Israel J. Math. 4 (1966), 59–61.Google Scholar
[6] Lindenstrauss, J.. Weakly compact sets-their topological properties and the Banach spaces they generate. Ann. of Math. Stud. 69 (1972), 235–273.Google Scholar
[7] Mcarthur, C. W., Singer, I. and Levin, M.. On the cones associated to biorthogonal systems and bases in Banach spaces. Caned. J. Math. 21 (1969), 1206–1217.CrossRefGoogle Scholar
[8] Singer, I.. Bases in Basch Spaces (Springer-Verlag, 1970).Google Scholar
[9] Tsekrekos, P. C.. Some applications of L-constants and M-constants on Banach Lattices. J. London Math. Soc. (2), 18 (1979), 133–139.Google Scholar