| 二维严格凸赋范空间单位球面间等距映射的线性延拓 |
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| 引用本文： | 王瑞东. 二维严格凸赋范空间单位球面间等距映射的线性延拓[J]. 数学学报, 2008, 51(5): 847-852 |
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| 作者姓名： | 王瑞东 |
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| 作者单位： | 天津南开大学数学学院 |
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| 摘 要： | 主要研究二维严格凸实赋范空间E和F的单位球面S_1(E)和S_1(F)之间的等距映射的线性延拓问题.利用二维严格凸赋范空间单位球面的性质得到:若等距映射V_0:S_1(E)→S_1(F)满足一定条件,则V_0可延拓为全空间E上的线性等距映射V:E→F.
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| 关 键 词： | Tingley问题 等距 线性延拓 严格凸赋范空间 |
| 收稿时间： | 2006-01-17 |
| 修稿时间： | 2007-08-20 |
On Linear Extension of Isometries Between the Unit Spheres of Two-Dimensional Strictly Convex Normed Space |
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| Affiliation: | School of Mathematical Sciences, Nankai University, Tianjin 300071 |
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| Abstract: | We study theextension of isometries between the unit spheres $S_1(E)$ and$S_1(F)$, where $E$ and $F$ are both two-dimensional strictlyconvex real normed spaces. Using the property of the unit sphereof two-dimensional strictly convex real normed space, we obtainthat if the isometry $V_0$ from $S_1(E)$ to $S_1(F)$ satisfiessome properties, then $V_0$ can be extended to be a real linearlyisometric map $V$ from $E$ to $F$. |
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| Keywords: | Tingley problem isometry linear extension strictly convex normed space |
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