2-Iso-reflexivity of pointed Lipschitz spaces
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2020-07-09Resumen
We show that in the case in which X and Y are uniformly concave complete pointed metric spaces, every 2-local isometry Δ from Lip_0(X) to Lip_0(Y) admits a representation as the sum of a weighted composition operator and a homogeneous Lipschitz functional on, at least, a subspace Y_0 of Y which is isometric to Y. Moreover, Δ is both linear and surjective when X is also separable.
Palabra/s clave
2-local isometry
Lipschitz function
Isometry
Weighted composition operator