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arXiv · 1807.11166

Symmetry of Birkhoff-James orthogonality of operators defined between infinite dimensional Banach spaces

Kallol Paul·Arpita Mal·Pawel Wójcik
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Abstract

We study left symmetric bounded linear operators in the sense of Birkhoff-James orthogonality defined between infinite dimensional Banach spaces. We prove that a bounded linear operator defined between two strictly convex Banach spaces is left symmetric if and only if it is zero operator when the domain space is reflexive and Kadets-Klee. We exhibit a non-zero left symmetric operator when the spaces are not strictly convex. We also study right symmetric bounded linear operators between infinite dimensional Banach spaces.

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Kallol Paul, Arpita Mal, Pawel Wójcik. 2018-07-30. Symmetry of Birkhoff-James orthogonality of operators defined between infinite dimensional Banach spaces. https://doi.org/10.1016/j.laa.2018.10.022

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