Chmieli�ski, J and Khurana, D and Sain, D (2021) Local Approximate Symmetry of Birkhoff�James Orthogonality in Normed Linear Spaces. In: Results in Mathematics, 76 (3).
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Abstract
Two different notions of approximate Birkhoff�James orthogonality in normed linear spaces have been introduced by Dragomir and Chmieli�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. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
| Item Type: | Journal Article |
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| Publication: | Results in Mathematics |
| Publisher: | Birkhauser |
| Additional Information: | The copyright for this article belongs to the authors. |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 02 Aug 2021 06:31 |
| Last Modified: | 02 Aug 2021 06:31 |
| URI: | http://eprints.iisc.ac.in/id/eprint/69045 |
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