Let (X, d) be a metric space and let \(\mathrm{Lip}(X,d) \) denote the complex algebra of all complex-valued bounded functions f on X for which f is a Lipschitz function on \(\mathrm{(X,d)}\). In this paper we give a complete description of all 2-local real and complex uniform isometries between \(\mathrm{Lip}(X,d) \) and \(\mathrm{Lip(Y},\rho \mathrm{)}\), where (X, d) and \((Y,\rho )\) are compact metric spaces. In particular, we show that every 2-local real (complex, respectively) uniform isometry from \(\mathrm{Lip}(X,d) \) to \(\mathrm{Lip(Y,}\rho \mathrm{)}\) is a surjective real (complex, respectively) linear uniform isometry.

中文翻译：

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复Lipschitz代数之间的2-局部一致等式

设（X，  d）是度量空间和让\（\ mathrm {唇}（X，d）\）表示的所有复数值的有界函数的复杂代数˚F上X为其˚F是李普希茨功能上\（ \ mathrm {（X，d）} \）。在本文中，我们对\（\ mathrm {Lip}（X，d）\）和\（\ mathrm {Lip（Y}，\ rho \ mathrm {） } \），其中（X，  d）和\（（Y，\ rho）\）是紧凑度量空间。特别是，我们证明了每个2局部实（分别为复数）均匀等距\（\ mathrm {Lip}（X，d）\）到\（\ mathrm {Lip（Y，} \ rho \ mathrm {）} \）是一个实射实数（分别为复杂的）线性均匀等距线。