
Journal of Convex Analysis 24 (2017), No. 3, 969985 Copyright Heldermann Verlag 2017 Diameter of Weak Neighborhoods and the RadonNikodym Property in OrliczLorentz Spaces Anna Kaminska Dept. of Mathematical Sciences, University of Memphis, Memphis, TN 381523240, U.S.A. kaminska@memphis.edu HyungJoon Tag Dept. of Mathematical Sciences, University of Memphis, Memphis, TN 381523240, U.S.A. htag@memphis.edu [Abstractpdf] Given an Orlicz $N$function $\varphi$ and a positive decreasing weight $w$, we present criteria for the diameter two property and for the RadonNikod\'ym property in the OrliczLorentz function and the sequence spaces $\Lambda_{\varphi,w}$ and $\lambda_{\varphi,w}$. We show that in the spaces $\Lambda_{\varphi,w}$ and $\lambda_{\varphi,w}$, equipped with the Luxemburg norm, the diameter of any relatively weakly open subset of the unit ball in these spaces is two if and only if $\varphi$ does not satisfy the appropriate $\Delta_2$condition, while they have the RadonNikod\'ym property if and only if $\varphi$ satisfies the appropriate $\Delta_2$condition. Keywords: Diameter two property, RadonNikodym property, OrliczLorentz space. MSC: 46B20, 46E30, 47B38 [ Fulltextpdf (182 KB)] for subscribers only. 