تقرير
Birkhoff-James classification of norm's properties
| العنوان: | Birkhoff-James classification of norm's properties |
|---|---|
| المؤلفون: | Guterman, Alexander, Kuzma, Bojan, Singla, Sushil, Zhilina, Svetlana |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Functional Analysis, 46B20, 05C63 |
| الوصف: | For an arbitrary normed space $\mathcal X$ over a field $\mathbb F \in \{ \mathbb R, \mathbb C \}$, we define the directed graph $\Gamma(\mathcal X)$ induced by Birkhoff-James orthogonality on the projective space $\mathbb P(\mathcal X)$, and also its nonprojective counterpart $\Gamma_0(\mathcal X)$. We show that, in finite-dimensional normed spaces, $\Gamma(\mathcal X)$ carries all the information about the dimension, smooth points, and norm's maximal faces. It also allows to determine whether the norm is a supremum norm or not, and thus classifies finite-dimensional abelian $C^\ast$-algebras among other normed spaces. We further establish the necessary and sufficient conditions under which the graph $\Gamma_0(\mathcal{R})$ of a (real or complex) Radon plane $\mathcal{R}$ is isomorphic to the graph $\Gamma_0(\mathbb F^2, \|\cdot\|_2)$ of the two-dimensional Hilbert space and construct examples of such nonsmooth Radon planes. Comment: Accepted for publications in AOT in The Special Issue Dedicated to Professor Chi-Kwong Li |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/2402.13416Test |
| رقم الانضمام: | edsarx.2402.13416 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |