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2-Local uniform isometries between complex Lipschitz algebras
Annals of Functional Analysis ( IF 1.2 ) Pub Date : 2020-01-01 , DOI: 10.1007/s43034-019-00011-6
Davood Alimohammadi , Reyhaneh Bagheri

Let (Xd) 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 (Xd) 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:

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˚FX为其˚F是李普希茨功能上\( \ mathrm {(X,d)} \)。在本文中,我们对\(\ mathrm {Lip}(X,d)\)\(\ mathrm {Lip(Y},\ rho \ mathrm {) } \),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\(\ mathrm {Lip}(X,d)\)\(\ mathrm {Lip(Y,} \ rho \ mathrm {)} \)是一个实射实数(分别为复杂的)线性均匀等距线。
更新日期:2020-01-01
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