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On approximate orthogonality and symmetry of operators in semi-Hilbertian structure

Sen, J and Sain, D and Paul, K (2021) On approximate orthogonality and symmetry of operators in semi-Hilbertian structure. In: Bulletin des Sciences Mathematiques, 170 .

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Official URL: https://doi.org/10.1016/j.bulsci.2021.102997


The purpose of the article is to generalize the concept of approximate Birkhoff-James orthogonality, in the semi-Hilbertian structure. Given a positive operator A on a Hilbert space H, we define (ϵ,A)-approximate orthogonality and (ϵ,A)-approximate orthogonality in the sense of Chmieliński and establish a relation between them. We also characterize (ϵ,A)-approximate orthogonality in the sense of Chmieliński for A-bounded and A-bounded compact operators. We further generalize the concept of right symmetric and left symmetric operators on a Hilbert space. The utility of these notions is illustrated by extending some of the previous results obtained by various authors in the setting of Hilbert spaces.

Item Type: Journal Article
Publication: Bulletin des Sciences Mathematiques
Publisher: Elsevier Masson s.r.l.
Additional Information: The copyright for this article belongs to the Authors.
Keywords: Approximate orthogonality; Compact operators; Left symmetric point; Norm attainment set; Positive operators; Right symmetric point
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 15 May 2023 10:03
Last Modified: 15 May 2023 10:03
URI: https://eprints.iisc.ac.in/id/eprint/81650

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