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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Abstract
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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