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arXiv · 2412.16584

Orthogonality induced by norm derivatives : A new geometric constant and symmetry

Souvik Ghosh·Kallol Paul·Debmalya Sain
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Abstract

In this article we study the difference between orthogonality induced by the norm derivatives (known as $\rho$-orthogonality) and Birkhoff-James orthogonality in a normed linear space $ \mathbb X$ by introducing a new geometric constant, denoted by $\Gamma(\mathbb{X}).$ We explore the relation between various geometric properties of the space and the constant $\Gamma(\mathbb{X}).$ We also investigate the left symmetric and right symmetric elements of a normed linear space with respect to $\rho$-orthogonality and obtain a characterization of the same. We characterize inner product spaces among normed linear spaces using the symmetricity of $\rho$-orthogonality. Finally, we provide a complete description of both left symmetric and right symmetric elements with respect to $\rho$-orthogonality for some particular Banach spaces.

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Souvik Ghosh, Kallol Paul, Debmalya Sain. 2024-12-21. Orthogonality induced by norm derivatives : A new geometric constant and symmetry. https://arxiv.org/abs/2412.16584

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