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Proceedings of the American Mathematical Society

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On the weak Radon-Nikodým property


Authors: Nassif Ghoussoub and Elias Saab
Journal: Proc. Amer. Math. Soc. 81 (1981), 81-84
MSC: Primary 46G10; Secondary 46B22
DOI: https://doi.org/10.1090/S0002-9939-1981-0589141-4
MathSciNet review: 589141
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Abstract: It is shown that in a Banach lattice the notions of the Radon-Nikodym property and the weak Randon-Nikodym property coincide. A problem of H. P. Lotz is solved affirmatively, namely, if the dual $ {Y^ * }$ of a Banach space $ Y$ is complemented in a Banach lattice $ E$ and if $ {l^1}$ does not embed into $ Y$ then $ {Y^ * }$ has the Radon-Nikodym property.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0589141-4
Keywords: (Weak) Radon-Nikodym property, Banach lattice
Article copyright: © Copyright 1981 American Mathematical Society