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...

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Detalles Bibliográficos
Autores: Cobollo-Gómez, Christian|||0000-0002-5901-5798, Guirao Sánchez, Antonio José|||0000-0002-1031-3954, Montesinos Santalucia, Vicente
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
Descripción
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/).