论文标题
进一步的结果是规范的角度等效性
Further results on angular equivalence of norms
论文作者
论文摘要
Kikianty和Sinnamon（2017）引入了规范的角度等效性，并且比通常的拓扑等效性更强。给定两个角度等效的规范，如果一个规范具有一定的几何特性，例如均匀的凸度，然后另一个规范也具有这样的特性。在本文中，我们在这个方向上显示了进一步的结果，即角度等效规范具有均匀的非质量的特性，并且角等效性保留了单位球的暴露点。还提供了有关角度等效规范的（同等）双重规范的讨论，如Kikianty and Sinnamon（2017）所述，对开放问题的部分答案给出了部分答案。
Angular equivalence of norms is introduced by Kikianty and Sinnamon (2017) and is a stronger notion than the usual topological equivalence. Given two angularly equivalent norms, if one norm has a certain geometrical property, e.g. uniform convexity, then the other norm also possesses such a property. In this paper, we show further results in this direction, namely angular equivalent norms share the property of uniform non-squareness, and that angular equivalence preserves the exposed points of the unit ball. A discussion on the (equivalence of the) dual norms of angularly equivalent norms is also given, giving a partial answer to an open problem as stated in the paper by Kikianty and Sinnamon (2017).
