Orthogonality and norm attainment of operators in semi-Hilbertian spaces

Sen, J and Sain, D and Paul, K (2021) Orthogonality and norm attainment of operators in semi-Hilbertian spaces. In: Annals of Functional Analysis, 12 (1).

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Abstract

We study the semi-Hilbertian structure induced by a positive operator A on a Hilbert space H. Restricting our attention to A- bounded positive operators, we characterize the norm attainment set and also investigate the corresponding compactness property. We obtain a complete characterization of the A- Birkhoff�James orthogonality of A- bounded operators under an additional boundedness condition. This extends the finite-dimensional Bhatia-S� emrl Theorem verbatim to the infinite-dimensional setting. © 2020, Tusi Mathematical Research Group (TMRG).

Item Type:	Journal Article
Publication:	Annals of Functional Analysis
Publisher:	Birkhauser
Additional Information:	The copyright for this article belongs to Author
Keywords:	Semi-Hilbertian structure Renorming Positive operators A-Birkhoff-James orthogonality Norm attainment set Compact operators
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	30 Dec 2021 04:34
Last Modified:	30 Dec 2021 04:34
URI:	http://eprints.iisc.ac.in/id/eprint/67263

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