本文研究实赋范空间E和F的单位球面S_1(E)和S_1(F)之间的等距映射线性延拓问题。得到:若T:S_1(E)→S_1(F)是一个满等距映射,且对于(?)x,y∈S_1(E),有‖T(x)-|λ|T(y)‖≤‖x-|λ|y‖,(?)λ∈R,则T可延拓为全空间上的实线性算子。

In this paper, we study the linear extension of isometries between the unit sphere S_1(E) of a real normed space E and the unit sphere S_1(F) of a real normed space F. We obtain that if T: S_1(E)→S_1(F) is a surjective isometry and for every x, y∈S_1(E), and real λ, we have ‖T(x)-|λ|T(y)‖≤‖x-|λ|y‖, then T can be extended to a real linear isometry on the whole space.