The isometrical extensions of 1-Lipschitz mappings on Gâteaux differentiability spaces

被引：0

作者：

GuangGui Ding

机构：

[1] Nankai University,School of Mathematical Sciences and LPMC

来源：

Science China Mathematics | 2011年 / 54卷

关键词：

1-Lipschitz mapping; linearly isometric extension; Gâteaux differentiability space; smooth point; 46A22; 46B02; 46B04; 46B20; 46B22;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let X and Y be real Banach spaces. Suppose that the subset sm[S1(X)] of the smooth points of the unit sphere S1(X) is dense in S1(X). If T0 is a surjective 1-Lipschitz mapping between two unit spheres, then, under some condition, T0 can be extended to a linear isometry on the whole space.

引用

页码：711 / 722

页数：11