The numerical index of 2-dimensional Lipschitz-free spaces
[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 int...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/207836 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/207836 |
| Access Level: | acceso abierto |
| Palabra clave: | Lipschitz-free Numerical index Numerical radius Geometry of Banach spaces MATEMATICA APLICADA |
| Sumario: | [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/). |
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