Norm derivatives and geometry of bilinear operators

Khurana, D and Sain, DP (2021) Norm derivatives and geometry of bilinear operators. In: Annals of Functional Analysis, 12 (3).

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Abstract

We study the norm derivatives in the context of Birkhoff�James orthogonality in real Banach spaces. As an application of this, we obtain a complete characterization of the left-symmetric points and the right-symmetric points in a real Banach space in terms of the norm derivatives. We obtain a complete characterization of strong Birkhoff�James orthogonality in �1n and ��n spaces. We also obtain a complete characterization of the orthogonality relation defined by the norm derivatives in terms of some newly introduced variation of Birkhoff�James orthogonality. We further study Birkhoff�James orthogonality, approximate Birkhoff�James orthogonality, smoothness and norm attainment of bounded bilinear operators between Banach spaces. © 2021, 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 Birkhauser
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	16 Sep 2021 09:08
Last Modified:	16 Sep 2021 09:08
URI:	http://eprints.iisc.ac.in/id/eprint/69602

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