Two kinds of convergent sequences on the real vector space m of all bounded sequences in a real normed space X were discussed in this paper,and we prove that they are equivalent,which improved the results of [1].
In this paper we introduce the isometric extension problem of isometric mappings between two unit spheres. Some important results of the related problems are outlined and the recent progress is mentioned.
Ding GuangGui School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China
This is such a article to consider an "into" isometric mapping between two unit spheres of two infinite dimensional spaces of different types. In this article, we find a useful condition (using the Krein-Milman property) under which an into-isometric mapping from the unit sphere of e(Γ) to the unit sphere of a normed space E can be linearly isometric extended.
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.
在这篇论文，我们看那 V 0 是否是在与 p 统一二个 AL p 空格的范围之间印射的 1-Lipschitz > 2 并且 ? V 0 (S 1 (L p )) 吗？V 0 (S 1 (L p )) ，然后， V 0 能被扩大到在整个空间定义的线性 isometry。如果 1 < p < 2 并且 V 0 是印射的鈥渁n ti-1-Lipschitz 鈥 ? ，那么， V 0 能线性地并且等大地也被扩大。关键词等轴的扩展 - AL p 空格 - 严格地凸的先生(2000 ) 题目分类 46A22 - 46B02 - 46B20 为高等教育(资助号码 20060055010 ) 的博士程序由中国(资助号码 10871101 )
