The numerical index of 2-dimensional Lipschitz-free spaces

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 [...

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Published in:Journal of mathematical analysis and applications 2024-10, Vol.538 (1), p.128333, Article 128333
Main Authors: Cobollo, Ch, Guirao, A.J., Montesinos, V.
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Language:English
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Geometry of Banach spaces
Lipschitz-free
Numerical index
Numerical radius
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description 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 [12,1], 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⊂Rn with n≥2 is any set with non-empty interior.
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subjects Geometry of Banach spaces
Lipschitz-free
Numerical index
Numerical radius
title The numerical index of 2-dimensional Lipschitz-free spaces
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