On the numerical index of polyhedral Banach spaces

Sain, Debmalya and Paul, Kallol and Bhunia, Pintu and Bag, Santanu (2019) On the numerical index of polyhedral Banach spaces. In: LINEAR ALGEBRA AND ITS APPLICATIONS, 577 . pp. 121-133.

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Abstract

The computation of the numerical index of a Banach space is an intriguing problem, even in case of two-dimensional real polyhedral Banach spaces. In this article we present a general method to estimate the numerical index of any finite dimensional real polyhedral Banach space, by considering the action of only finitely many functionals, on the unit sphere of the space. We further obtain the exact numerical index of a family of 3-dimensional polyhedral Banach spaces for the first time, in order to illustrate the applicability of our method.

Item Type:	Journal Article
Publication:	LINEAR ALGEBRA AND ITS APPLICATIONS
Publisher:	ELSEVIER SCIENCE INC
Additional Information:	copyright for this article belongs to ELSEVIER SCIENCE INC
Keywords:	Polyhedral Banach spaces; Numerical radius; Numerical index; Face of a polyhedron
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	27 Aug 2019 06:16
Last Modified:	27 Aug 2019 06:16
URI:	http://eprints.iisc.ac.in/id/eprint/63286

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