The approximation property for spaces of Lipschitz functions with the bounded weak* topology
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Jiménez Vargas, AntonioDate
2016-01-10Abstract
Let X be a pointed metric space and let Lip_0(X) be the space of all scalar-valued Lipschitz functions on X which vanish at the basepoint. We prove that Lip_0(X) with the bounded weak* topology τ_{bw∗} 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 \gamma\tau_{\gamma} on Lip_0(X,F) such that the Lipschitz transpose mapping f→f^t is a topological isomorphism from (Lip_(X,F),\gamma\tau_{\gamma}) to (Lip_0(X), τ_{bw∗})\epsilon F .
Palabra/s clave
Lipschitz spaces
Approximation property
Tensor product
epsilon product