This is an announcement for the paper “Diameter of weak neighborhoods and the Radon-Nikodym property in Orlicz-Lorentz spaces” by Anna Kamińskahttp://arxiv.org/find/math/1/au:+Kaminska_A/0/1/0/all/0/1, Hyung-Joon Taghttp://arxiv.org/find/math/1/au:+Tag_H/0/1/0/all/0/1.
Abstract: Given an Orlicz convex function $\phi$ and a positive weight $w$ we present criteria of diameter two property and of Radon-Nikodym property in the Orlicz-Lorentz function and sequence spaces, $\Lambda_{\phi, w}$ and $\lambda_{\phi, w}$, respectively. We show that in the spaces $\Lambda_{\phi, w}$ or $\lambda_{\phi, w}$ equipped with the Luxemburg norm, the diameter of any relatively weakly subset of the unit ball in these spaces is two if and only if $\phi$ does not satisfy the appropriate growth condition $\Delta_2$, while they do have the Radon-Nikodym property if and only if $\phi$ satisfies the appropriate condition $\Delta_2$.
The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1606.00909