2-iso-reflexivity of pointed Lipschitz spaces. (English) Zbl 1467.46010
Summary: We show that in the case in which \(X\) and \(Y\) are uniformly concave complete pointed metric spaces, every 2-local isometry \(\Delta\) from \(\text{Lip}_0(X)\) to \(\text{Lip}_0(Y)\) 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, \(\Delta\) is both linear and surjective when \(X\) is also separable.
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