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On symmetric points with respect to the numerical radius norm

Ghosh, S and Mal, A and Paul, K and Sain, D (2023) On symmetric points with respect to the numerical radius norm. In: Banach Journal of Mathematical Analysis, 17 (4).

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Official URL: https://doi.org/10.1007/s43037-023-00290-1


We study left symmetric and right symmetric points with respect to the numerical radius orthogonality (respectively, known as nr-left symmetric operators and nr-right symmetric operators) in the setting of both Hilbert spaces and Banach spaces. We prove that a bounded linear operator T on a complex Hilbert space is nr-left symmetric if and only if T is the zero operator, provided that T attains its numerical radius. We also prove that a nonzero compact normal operator on an infinite-dimensional complex Hilbert space cannot be nr-right symmetric. We then study nr-left symmetry and nr-right symmetry in the setting of Banach spaces and obtain separate necessary and sufficient conditions for the same. Next, we obtain complete characterizations of nr-left and nr-right symmetric operators on some particular Banach spaces. © 2023, Tusi Mathematical Research Group (TMRG).

Item Type: Journal Article
Publication: Banach Journal of Mathematical Analysis
Publisher: Birkhauser
Additional Information: The copyright for this article belongs to the Birkhauser.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 07 Nov 2023 11:09
Last Modified: 07 Nov 2023 11:09
URI: https://eprints.iisc.ac.in/id/eprint/83029

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