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

2016/06/02 by Anna Kamińska, Kamińska, Anna, Hyung-Joon Tag +1
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.1606.00909

openalex publication_date 2016/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given an Orlicz N-function \φ and a positive decreasing weight w,\nwe present criteria of the diameter two property and of the Radon-Nikod 'ym\nproperty in Orlicz-Lorentz function and sequence spaces \Λ_\φ,w\nand \λ_\φ,w. We show that in the spaces \Λ_\φ,w or\n\λ_\φ,w equipped with the Luxemburg norm, the diameter of any\nrelatively weakly subset of the unit ball in these spaces is two if and only if\n\φ does not satisfy the appropriate \Δ₂ condition, while they\nhave the Radon-Nikod 'ym property if and only if \φ satisfies the\nappropriate \Δ₂ condition.\n

Citations

• Remarks on diameter 2 properties

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