Wang, Rui Dong et Huang, Xu Jian, Isometries and additive mapping on the unit spheres of normed spaces, Acta mathematica Sinica. English series (Print) , 33(10), 2017, pp. 1431-1442
In this paper, we investigate isometric extension problem in general normed space. We prove that an isometry between spheres can be extended to a linear isometry between the spaces if and only if the natural positive homogeneous extension is additive on spheres. Moreover, this conclusion still holds provided that the additivity holds on a restricted domain of spheres.