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：
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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.
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页码：711 / 722
页数：11
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