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Birkhoff–James Orthogonality in Complex Banach Spaces and Bhatia–Šemrl Theorem Revisited

Roy, S and Bagchi, S and Sain, D (2022) Birkhoff–James Orthogonality in Complex Banach Spaces and Bhatia–Šemrl Theorem Revisited. In: Mediterranean Journal of Mathematics, 19 (2).

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Official URL: https://doi.org/10.1007/s00009-022-01979-7

Abstract

We explore Birkhoff–James orthogonality of two elements in a complex Banach space 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–Šemrl Theorem on orthogonality of linear operators.

Item Type: Journal Article
Publication: Mediterranean Journal of Mathematics
Publisher: Birkhauser
Additional Information: The copyright for this article belongs to the Birkhauser.
Keywords: Bhatia–Šemrl theorem; Birkhoff–James orthogonality; complex Banach spaces; smoothness; Toeplitz–Hausdorff theorem
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 24 Jun 2022 12:10
Last Modified: 24 Jun 2022 12:10
URI: https://eprints.iisc.ac.in/id/eprint/73710

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