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

@inproceedings{Roy2021BirkhoffJamesOI, title={Birkhoff-James orthogonality in complex Banach spaces and Bhatia-\v\{S\}emrl Theorem revisited}, author={Saikat Roy and Satya Bagchi and Debmalya Sain}, year={2021} }

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 nonsmooth point in a complex Banach space. As a concrete outcome of our study, we obtain a new proof of the Bhatia-Šemrl Theorem on orthogonality of linear operators.

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