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arXiv · 1606.00909

Diameter of weak neighborhoods and the Radon-Nikodym property in Orlicz-Lorentz spaces

Anna Kamińska·Hyung-Joon Tag
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Abstract

Given an Orlicz $N$-function $\varphi$ and a positive decreasing weight $w$, we present criteria of the diameter two property and of the Radon-Nikod\'ym property in Orlicz-Lorentz function and sequence spaces $\Lambda_{\varphi,w}$ and $\lambda_{\varphi,w}$. We show that in the spaces $\Lambda_{\varphi,w}$ or $\lambda_{\varphi,w}$ 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 $\varphi$ 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.

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Anna Kamińska, Hyung-Joon Tag. 2016-06-02. Diameter of weak neighborhoods and the Radon-Nikodym property in Orlicz-Lorentz spaces. https://arxiv.org/abs/1606.00909

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