Relationships between K-monotonicity and rotundity properties with application

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:465

Article

Ciesielski, Maciej¹ 

[1] Poznan Univ Tech, Inst Math, Piotrowo 3A, PL-60965 Poznan, Poland

关键词: Decreasing (increasing) uniform;    K-monotonicity;    K-order continuity;    Strict K-rnonotonicity;    Fully k-rotundity;    Symmetric space;    The best approximation;   

DOI  :  10.1016/j.jmaa.2018.05.008

来源: Elsevier

【 摘 要 】

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 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 F-p,F-omega and K-order continuity in Orlicz spaces L-psi. Finally, we show an application of discussed geometric properties to the approximation theory. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free