Numerical radius and a notion of smoothness in the space of bounded linear operators

Roy, S and Sain, D (2021) Numerical radius and a notion of smoothness in the space of bounded linear operators. In: Bulletin des Sciences Mathematiques, 173 .

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Abstract

We observe that the classical notion of numerical radius gives rise to a notion of smoothness in the space of bounded linear operators on certain Banach spaces, whenever the numerical radius is a norm. We characterize Birkhoff-James orthogonality in the space of bounded linear operators on a finite-dimensional Banach space, endowed with the numerical radius norm. Some examples are also discussed to illustrate the geometric differences between the numerical radius norm and the usual operator norm, from the viewpoint of operator smoothness. © 2021 Elsevier Masson SAS

Item Type:	Journal Article
Publication:	Bulletin des Sciences Mathematiques
Publisher:	Elsevier Masson s.r.l.
Additional Information:	The copyright for this article belongs to Author
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	28 Nov 2021 08:04
Last Modified:	28 Nov 2021 08:04
URI:	http://eprints.iisc.ac.in/id/eprint/70406

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