On the Class of Banach Spaces with James Constant \({\sqrt{2}}\) : Part II
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- 作者：Naoto Komuro ; Kichi-Suke Saito ; Ryotaro Tanaka
- 关键词：James constant ; isosceles orthogonality ; rotation invariant norm ; absolute norm
- 刊名：Mediterranean Journal of Mathematics
- 出版年：2016
- 出版时间：December 2016
- 年：2016
- 卷：13
- 期：6
- 页码：4039-4061
- 全文大小：618 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics - 出版者：Birkh盲user Basel
- ISSN：1660-5454
- 卷排序：13
文摘
The class of two-dimensional normed spaces with James constant \({\sqrt{2}}\) is studied. It is shown that, if the norm is \({\pi/2}\)-rotation invariant, then its James constant is \({\sqrt{2}}\) if and only if the norm is \({\pi/4}\)-rotation invariant. We also present a characterization of \({\pi/4}\)-rotation invariant norms using some properties of certain convex functions on the unit interval, which allow us to easily construct norms the James constant of which are \({\sqrt{2}}\). Moreover, two important examples are given, which show that neither absoluteness, symmetry nor \({\pi/2}\)-rotation invariance can be a characteristic property of the norms with James constant \({\sqrt{2}}\).