On the weak Radon-Nikodým property

Ghoussoub, Nassif; Saab, Elias

doi:10.1090/S0002-9939-1981-0589141-4

On the weak Radon-Nikodým property
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by Nassif Ghoussoub and Elias Saab PDF

Proc. Amer. Math. Soc. 81 (1981), 81-84 Request permission

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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