| 单位球面间等距映射的线性延拓 |
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| 引用本文： | 方习年,王建华.单位球面间等距映射的线性延拓[J].数学学报,2005,48(6):1109-1112. |
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| 作者姓名： | 方习年 王建华 |
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| 作者单位： | [1]南京审计学院应用数学系,南京210029 [2]安徽师范大学数学系,芜湖241000 |
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| 基金项目： | 安徽省教育厅科研项目（2002kj068） |
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| 摘 要： | 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。
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| 关 键 词： | 等距映射 等距延拓 Tingley问题 |
| 文章编号： | 0583-1431（2005）06-1109-04 |
| 收稿时间： | 2004-12-26 |
| 修稿时间： | 2004-12-262005-04-12 |
On Linear Extension of Isometries Between the Unit Spheres |
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| Xi Nian FANG, Jian Hua WANG.On Linear Extension of Isometries Between the Unit Spheres[J].Acta Mathematica Sinica,2005,48(6):1109-1112. |
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| Authors: | Xi Nian FANG Jian Hua WANG |
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| Institution: | 1 Department of Applied Mathematics, Nanjing Audit University, Nanjing 210029, P. R. China;2 Department of Mathematics, Anhui Normal University, Wuhu 241000, P. R. China |
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| Abstract: | 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. |
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| Keywords: | Isometry Extension of isometry Tingley problem |
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