Hostname: page-component-5c6d5d7d68-7tdvq Total loading time: 0 Render date: 2024-08-15T18:34:22.504Z Has data issue: false hasContentIssue false
  • English
  • Français

Strongly exposed points and a characterization of l1 (Γ) by the Schur property

Published online by Cambridge University Press:  20 January 2009

Ioannis A. Polyrakis
Ioannis A. Polyrakis
Affiliation:
National Technical University, Department of Mathematics, Zografou Campus 157 73, Athens, Greece
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we study the existence of strongly exposed points in unbounded closed and convex subsets of the positive cone of ordered Banach spaces and we prove the following characterization for the space l1(Γ): A Banach lattice X is order-isomorphic to l1(Γ) iff X has the Schur property and X* has quasi-interior positive elements.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 30 , Issue 3 , October 1987 , pp. 397 - 400
Copyright
Copyright © Edinburgh Mathematical Society 1987

References

REFERENCES

1.Bourgin, R. D., Geometric Aspects of Convex Sets with the Radon-Nikodym Property (Lecture Notes in Mathematics 993).Google Scholar
2.Ghoussoub-M., N.Talagrand, , Order dentability and the Radon-Nikodym property in Banach lattices, Math. Ann. 243 (1979), 217–225.CrossRefGoogle Scholar
3.Polyrakis, I. A., Extreme points of unbounded, closed and convex sets in Banach spaces, Math. Proc. Cambridge Philos. Soc. 95 (1984), 319–323.CrossRefGoogle Scholar
4.Polyrakis, I. A., Strongly exposed points in bases for the positive cone of ordered Banach spaces and characterizations of l 1(Γ), Proc. Edinburgh Math. Soc. 29, (1986), 271–282.CrossRefGoogle Scholar
5.Schaefer, H. H., Banach Lattices and Positive Operators (Springer-Verlag, 1974).CrossRefGoogle Scholar