Further results on angular equivalence of norms
Functional Analysis
2022-02-01 v2
Abstract
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).
Keywords
Cite
@article{arxiv.2201.02865,
title = {Further results on angular equivalence of norms},
author = {Eder Kikianty},
journal= {arXiv preprint arXiv:2201.02865},
year = {2022}
}