Abstract
We construct a separable dual Banach latticeE such that no non-trivial order interval of its dual is weakly compact. HenceE has the Radon-Nikodym property without being in some sense a dual in a natural way.
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J. Bourgain and F. Delbaen, A special class of −α spaces, Acta Math., to appear.
J. Diestel,Geometry of Banach Spaces — Selected Topics, Lecture Notes in Math., Springer Verlag, pp. 485.
H. Lotz,The Radon-Nikodym property in Banach lattices, to appear.
P. W. McCartney and R. C. O’Brien,A separable Banach space with the Radon-Nikodym property which is not isomorphic to a subspace of a separable dual, to appear.
M. Talagrand,fr|Sur la propriété de Radon-Nikodym dans les espaces de Banach reticulés, C. R. Acad. Sci.288 (1979), 907–910.
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The final draft of this paper was written while the author held a grant from NATO to visit the Ohio State University.
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Talagrand, M. Dual banach lattices and Banach lattices with the Radon-Nikodym property. Israel J. Math. 38, 46–50 (1981). https://doi.org/10.1007/BF02761847
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DOI: https://doi.org/10.1007/BF02761847