Orthogonality and smoothness induced by the norm derivatives

Sain, D (2021) Orthogonality and smoothness induced by the norm derivatives. In: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, 115 (3).

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Abstract

We study the concepts of orthogonality and smoothness in normed linear spaces, induced by the derivatives of the norm function. We obtain analytic characterizations of the said orthogonality relations in terms of support functionals in the dual space. We also characterize the related notions of local smoothness and establish its connection with the corresponding orthogonality set, which is analogous to the well-known relation between the Birkhoff�James orthogonality and the classical notion of smoothness. The similarities and the differences between the various notions of smoothness are illustrated by considering some particular examples, including K(H) , the Banach space of all compact operators on a Hilbert space H. © 2021, The Royal Academy of Sciences, Madrid.

Item Type:	Journal Article
Publication:	Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Publisher:	Springer-Verlag Italia s.r.l.
Additional Information:	The copyright for this article belongs to Springer-Verlag Italia s.r.l.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	17 Aug 2021 12:05
Last Modified:	17 Aug 2021 12:05
URI:	http://eprints.iisc.ac.in/id/eprint/69164

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