Isometric representations of weighted spaces of little Lipschitz functions
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2018-02-21Resumen
Given a compact pointed metric space X and a weight v on the complement of the diagonal set in X × X, we prove that the Banach space lip_v(X) of all weighted little Lipschitz scalar-valued functions on X vanishing at the basepoint, equipped with the weighted Lipschitz norm, embeds almost isometrically into c_0. This result has many consequences on the structure of those Banach spaces and their duals. Moreover, we prove that this isomorphism can never be an isometric embedding whenever X is a T-balanced subset containing 0 and compact for some metrizable topology of a complex Banach space and v is a radial 0-weight.
Palabra/s clave
Lipschitz function
Little Lipschitz function
Weighted Banach space