The approximation property for spaces of Lipschitz functions with the bounded weak* topology

• Autores: Antonio Jiménez Vargas
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 2, 2018, págs. 637-654
• Idioma: inglés
• DOI: 10.4171/RMI/999
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• Resumen

  • Let X be a pointed metric space and let Lip0(X) be the space of all scalar-valued Lipschitz functions on X which vanish at the base point. We prove that Lip0(X) with the bounded weak* topology τbw∗ has the approximation property if and only if the Lipschitz-free Banach space F(X) has the approximation property if and only if, for each Banach space F, each Lipschitz operator from X into F can be approximated by Lipschitz finite-rank operators within the unique locally convex topology γτγ on Lip0(X,F) such that the Lipschitz transpose mapping f↦ft is a topological isomorphism from Lip0(X,F),γτγ) to (Lip0(X),τbw∗)ϵF.