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arXiv · 2109.12775

Birkhoff-James orthogonality in complex Banach spaces and Bhatia-\v{S}emrl Theorem revisited

Saikat Roy·Satya Bagchi·Debmalya Sain
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Abstract

We explore Birkhoff-James orthogonality of two elements in a complex Banach space by using the directional approach. Our investigation illustrates the geometric distinctions between a smooth point and a non-smooth point in a complex Banach space. As a concrete outcome of our study, we obtain a new proof of the Bhatia-\v{S}emrl Theorem on orthogonality of linear operators.

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Saikat Roy, Satya Bagchi, Debmalya Sain. 2021-09-27. Birkhoff-James orthogonality in complex Banach spaces and Bhatia-\v{S}emrl Theorem revisited. https://arxiv.org/abs/2109.12775

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