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arXiv · 1802.09268

Relationships between K-monotonicity and rotundity properties with application

Maciej Ciesielski
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Abstract

In this paper we investigate a relationship between fully k-rotundity properties, uniform K-monotonicity properties, reflexivity and K-order continuity in a symmetric spaces E. We also answer a crucial question whether fully k-rotundity properties might be restricted in definition to E^d the positive cone of all nonnegative and decreasing elements of E. We present a complete characterization of decreasing uniform K-monotonicity and K-order continuity in E. It is worth mentioning that we also establish several auxiliary results describing reflexivity in Lorentz spaces and K-order continuity in Orlicz spaces. Finally, we show an application of discussed geometric properties to the approximation theory.

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Maciej Ciesielski. 2018-02-26. Relationships between K-monotonicity and rotundity properties with application. https://arxiv.org/abs/1802.09268

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