On the numerical index of polyhedral Banach spaces
Functional Analysis
2024-08-13 v2
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.
Keywords
Cite
@article{arxiv.1809.04778,
title = {On the numerical index of polyhedral Banach spaces},
author = {Debmalya Sain and Kallol Paul and Pintu Bhunia and Santanu Bag},
journal= {arXiv preprint arXiv:1809.04778},
year = {2024}
}