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 .

中文翻译：

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正交性的局部保持及其在等轴测中的应用

我们研究了有限维 Banach 空间上的线性算子在一点处的 Birkhoff-James 正交性的局部保持，并说明了其对于理解算子在相关空间的几何形状方面的作用的重要性。特别是，它表明这样的研究与巴拿赫空间的单位球的 k 平滑性和极值性质的保存有关。作为在这个方向上获得的结果的应用，我们获得了一些多面体 Banach 空间上著名的 Blanco-Koldobsky-Turnsek 等距表征的改进，包括 。