| Autor: |
Sain, Debmalya, Manna, Jayanta, Paul, Kallol |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
Linear Algebra Appl. 690 (2024), 112-131 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1016/j.laa.2024.03.004 |
| Popis: |
We investigate the local preservation of Birkhoff-James orthogonality at a point by a linear operator on a finite-dimensional Banach space and illustrate its importance in understanding the action of the operator in terms of the geometry of the concerned spaces. In particular, it is shown that such a study is related to the preservation of k-smoothness and the extremal properties of the unit ball of a Banach space. As an application of the results obtained in this direction, we obtain a refinement of the well-known Blanco-Koldobsky-Turnsek characterization of isometries on some polyhedral Banach spaces, including $ \ell_{\infty}^n, \ell_1^n. $ |
| Databáze: |
arXiv |
| Externí odkaz: |
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