K-单调性与凸性的关系及其应用
Relationships between K-monotonicity and rotundity properties with application
摘要：
本文研究了对称空间E中完全k-凸性、一致k-单调性、自反性和k-阶连续性之间的关系。我们还回答了一个关键的问题，是否完全k-凸性的性质可以在定义上限制到E^d，E ^d是E的所有非负和递减元素的正锥。本文给出了E中一致单调性和K阶连续性的一个完整刻画。值得一提的是，我们还建立了描述Lorentz空间中自反性和Orlicz空间中K阶连续性的几个辅助结果。最后，我们讨论的几何性质的应用程序的逼近论。
英文摘要：
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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