The numerical index of 2-dimensional Lipschitz-free spaces

Abstract

[EN] We provide the explicit formula for the numerical index of any 2 -dimensional Lipschitz-free space, also giving the construction of operators attaining this value as its numerical radius. As a consequence, the numerical index of 2 -dimensional Lipschitz-free spaces can take any value of the interval [ 1 2 , 1], and this whole range of numerical indices can be attained by taking 2 -dimensional subspaces of any Lipschitz-free space of the form F( A), where A subset of R n with n >= 2 is any set with non-empty interior. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http:// creativecommons .org /licenses /by -nc -nd /4 .0/).