Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899488 | Journal of Mathematical Analysis and Applications | 2018 | 25 Pages |
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 Îp,w and K-order continuity in Orlicz spaces LÏ. Finally, we show an application of discussed geometric properties to the approximation theory.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Maciej Ciesielski,