On the numerical index of polyhedral Banach spaces
arXiv:1809.04778 · doi:10.1016/j.laa.2019.04.024
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 -dimensional polyhedral Banach spaces for the first time, in order to illustrate the applicability of our method.