On the numerical index of polyhedral Banach spaces

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. (C) 2019 Elsevier Inc. All rights reserved.