| Extension of Isometries Between the Unit Spheres of Normed Space E and C（Ω） |
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| 作者姓名： | Xi Nian FANG Jian Hua WANG |
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| 作者单位： | [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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| 摘 要： | In this paper, we study the extension of isometries between the unit spheres of normed space E and C（Ω）. We obtain that any surjective isometry between the unit spheres of normed space E and C（Ω） can be extended to be a linear isometry on the whole space E and give an affirmative answer to the corresponding Tingley＇s problem （where Ω be a compact metric space）.
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| 关 键 词： | 等容映射 等容扩展 Tingley问题 球面单位 |
| 收稿时间： | 2005-04-15 |
| 修稿时间： | 2005-04-152005-10-31 |
Extension of Isometries Between the Unit Spheres
of Normed Space E and C (Ω) |
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| Xi Nian FANG Jian Hua WANG.Extension of Isometries Between the Unit Spheres
of Normed Space E and C (Ω)[J].Acta Mathematica Sinica,2006,22(6):1819-1824. |
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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 extension of isometries between the unit spheres of normed
space E and C(Ω). We obtain that any surjective isometry between the unit spheres of normed space
E and C(Ω) can be extended to be a linear isometry on the whole space E and give an affirmative
answer to the corresponding Tingley’s problem (where Ω be a compact metric space). |
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| Keywords: | isometric mapping isometric extension Tingley’ s problem |
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