2-local isometries on vector-valued Lipschitz function spaces
Ya-Shu Wang
Department of Applied Mathematics
National Chung Hsing University
yashu@nchu.edu.tw
Let `E` and `F` be Banach spaces. Let `\mathcal{S}` be a subset of the space `L(E,F)` of all continuous linear maps from `E` into `F`. A (non-necessarily linear nor continuous) mapping `\Delta:E\to F` is a 2-local `\mathcal{S}`-map, if for any `x,y\in E`, there exists `T_{x,y}\in\mathcal{S}`, depending on `x` and `y`, such that`\Delta(x)=T_{x,y}(x)" and "\Delta(y)=T_{x,y}(y).`