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arXiv · 1711.03802

An extension of orthogonality relations based on norm derivatives

A. Zamani·M. S. Moslehian
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Abstract

We introduce the relation ${\rho}_{\lambda}$-orthogonality in the setting of normed spaces as an extension of some orthogonality relations based on norm derivatives, and present some of its essential properties. Among other things, we give a characterization of inner product spaces via the functional ${\rho}_{\lambda}$. Moreover, we consider a class of linear mappings preserving this new kind of orthogonality. In particular, we show that a linear mapping preserving ${\rho}_{\lambda}$-orthogonality has to be a similarity, that is, a scalar multiple of an isometry.

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A. Zamani, M. S. Moslehian. 2017-11-10. An extension of orthogonality relations based on norm derivatives. https://doi.org/10.1093/qmath%2Fhay048

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