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arXiv · 2304.13183

The numerical index of $2$-dimensional Lipschitz-free spaces

Ch. Cobollo·A. J. Guirao·V. Montesinos
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Abstract

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 $[\frac{1}{2},1]$, and this whole range of numerical indices can be attained by taking $2$-dimensional subspaces of any Lipschitz-free space of the form $\mathcal{F}(A)$, where $A\subset {\mathbb{R}}^n$ with $n\geq 2$ is any set with non-empty interior.

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Ch. Cobollo, A. J. Guirao, V. Montesinos. 2023-04-25. The numerical index of $2$-dimensional Lipschitz-free spaces. https://arxiv.org/abs/2304.13183

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