The approximation property for spaces of Lipschitz functions with the bounded weak* topology
Antonio Jiménez-Vargas
Universidad de Almería, Spain
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Abstract
Let be a pointed metric space and let Lip be the space of all scalar-valued Lipschitz functions on which vanish at the base point. We prove that Lip with the bounded weak* topology has the approximation property if and only if the Lipschitz-free Banach space has the approximation property if and only if, for each Banach space , each Lipschitz operator from into can be approximated by Lipschitz finite-rank operators within the unique locally convex topology on Lip such that the Lipschitz transpose mapping is a topological isomorphism from Lip to (Lip.
Cite this article
Antonio Jiménez-Vargas, The approximation property for spaces of Lipschitz functions with the bounded weak* topology. Rev. Mat. Iberoam. 34 (2018), no. 2, pp. 637–654
DOI 10.4171/RMI/999