On the numerical index of polyhedral Banach spaces

Debmalya Sain,Kallol Paul,Pintu Bhunia,Santanu Bag

doi:10.1016/j.laa.2019.04.024

On the numerical index of polyhedral Banach spaces

Debmalya Sain, Kallol Paul + Show 2 more

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https://doi.org/10.1016/j.laa.2019.04.024

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Journal: Linear Algebra and Its Applications	Publication Date: Apr 26, 2019
Citations: 21	License type: publisher-specific-oa

Affiliation: Jadavpur University, Polytechnic University of Bari, Ramakrishna Mission Vivekananda Educational and Research Institute, Indian Institute of Science Bangalore

#Polyhedral Banach Spaces #Finite-dimensional Banach Space + Show 8 more

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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.

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