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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Bibliographic Details
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.
Format: Article
Language:English
Subjects:
Geometry of Banach spaces
Lipschitz-free
Numerical index
Numerical radius
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Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2024.128333