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Some remarks on Birkhoff–James orthogonality of linear operators

Sain, D and Mal, A and Paul, K (2020) Some remarks on Birkhoff–James orthogonality of linear operators. In: Expositiones Mathematicae, 38 (1). pp. 138-147.

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Official URL: https://doi.org/10.1016/j.exmath.2019.01.001


We study Birkhoff–James orthogonality of compact (bounded) linear operators between Hilbert spaces and Banach spaces. Applying the notion of semi-inner-products in normed linear spaces and some related geometric ideas, we generalize and improve some of the recent results in this context. In particular, we obtain a characterization of Euclidean spaces and also prove that it is possible to retrieve the norm of a compact (bounded) linear operator (functional) in terms of its Birkhoff–James orthogonality set. We also present some best approximation type results in the space of bounded linear operators. © 2019 Elsevier GmbH

Item Type: Journal Article
Publication: Expositiones Mathematicae
Publisher: Elsevier GmbH
Additional Information: The copyright for this article belongs to the Authors.
Keywords: Best approximation; Birkhoff–James orthogonality; Linear operator; Semi-inner-product
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 24 Jan 2023 11:13
Last Modified: 24 Jan 2023 11:13
URI: https://eprints.iisc.ac.in/id/eprint/79427

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