Article ID Journal Published Year Pages File Type
8899488 Journal of Mathematical Analysis and Applications 2018 25 Pages PDF
Abstract
In this paper we investigate a relationship between fully k-rotundity properties, uniform K-monotonicity properties, reflexivity and K-order continuity in symmetric spaces E. We also answer a crucial question whether fully k-rotundity properties might be restricted in definition to Ed 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 Γp,w and K-order continuity in Orlicz spaces Lψ. Finally, we show an application of discussed geometric properties to the approximation theory.
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Physical Sciences and Engineering Mathematics Analysis
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