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

Abstract

Given an Orlicz convex function φ and a positive weight w we present criteria of diameter two property and of Radon-Nikodým property in the Orlicz-Lorentz function and sequence spaces, Λφ,w and λφ,w, respectively. We show that in the spaces Λφ,w or λφ,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 φ does not satisfy the appropriate growth condition Δ2, while they do have the Radon-Nikodým property if and only if φ satisfies the appropriate condition Δ2.

Publication Title

Journal of Convex Analysis

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