Geodesic
Diameter of Weak Neighborhoods and the Radon-Nikodym Property in Orlicz-Lorentz Spaces
Journal of convex analysis, Tome 24 (2017) no. 3, pp. 969-985
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Given an Orlicz $N$-function $\varphi$ and a positive decreasing weight $w$, we present criteria for the diameter two property and for the Radon-Nikod\'ym property in the Orlicz-Lorentz 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 Radon-Nikod\'ym property if and only if $\varphi$ satisfies the appropriate $\Delta_2$-condition.
Classification : 46B20, 46E30, 47B38
Mots-clés : Diameter two property, Radon-Nikodym property, Orlicz-Lorentz space 
@article{JCA_2017_24_3_JCA_2017_24_3_a13,
     author = {A. Kaminska and H.-J. Tag},
     title = {Diameter of {Weak} {Neighborhoods} and the {Radon-Nikodym} {Property} in {Orlicz-Lorentz} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {969--985},
     year = {2017},
     volume = {24},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_3_JCA_2017_24_3_a13/}
}
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A. Kaminska; H.-J. Tag. Diameter of Weak Neighborhoods and the Radon-Nikodym Property in Orlicz-Lorentz Spaces. Journal of convex analysis, Tome 24 (2017) no. 3, pp. 969-985. http://geodesic.mathdoc.fr/item/JCA_2017_24_3_JCA_2017_24_3_a13/