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arXiv · 2012.08162

Local approximate symmetry of Birkhoff-James orthogonality in normed linear spaces

Jacek Chmieliński·Divya Khurana·Debmalya Sain
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Abstract

Two different notions of approximate Birkhoff-James orthogonality in nor\-med linear spaces have been introduced by Dragomir and Chmie\-li\'n\-ski. In the present paper we consider a global and a local approximate symmetry of the Birkhoff-James orthogonality related to each of the two definitions. We prove that the considered orthogonality is approximately symmetric in the sense of Dragomir in all finite-dimensional Banach spaces. For the other case, we prove that for finite-dimensional polyhedral Banach spaces, the approximate symmetry of the orthogonality is equivalent to some newly introduced geometric property. Our investigations complement and extend the scope of some recent results on a global approximate symmetry of the Birkhoff-James orthogonality.

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Jacek Chmieliński, Divya Khurana, Debmalya Sain. 2020-12-15. Local approximate symmetry of Birkhoff-James orthogonality in normed linear spaces. https://arxiv.org/abs/2012.08162

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