On local preservation of orthogonality and its application to isometries
Linear Algebra and its Applications(2024)
摘要
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 ℓ∞n,ℓ1n.
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关键词
Finite-dimensional Banach spaces,Polyhedral Banach spaces,Linear operators,Birkhoff-James orthogonality,k-smoothness,Isometry
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