Banach空间上单位球面间的1-Lipschitz映射

1-Lipschitz Mappings Between Unit Spheres of Banach Spaces

讨论了单位球面间非满1-Lipscllitz映射的延拓问题并得到:在一定条件下,每个1-Lipschitz映射都能被延拓成全空间上的实线性等距映射.这是第一次在一般Banach空间上研究1-Lipschitz映射延拓问题.

We discuss the extension problem of non-surjective 1-Lipschitz mappings between unit spheres, and obtain that, under some conditions, every 1-Lipschitz map can be extended to be a real linear isometric mapping on the whole space. This is the first time we study the 1-Lipschitz map extension problem on ＂general＂ Banach spaces.