| The Isometric Extension of an Into Mapping from the Unit Sphere S（t（2）^∞） to S（L^1（μ）） |
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| 基金项目： | This paper is supported by The National Natural Science Foundation of China （10571090） and The Research Fund for the Doctoral Program of Higher Education （20010055013） |
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| 摘 要： | This is the first paper to consider the isometric extension problem of an into-mapping between the unit spheres of two different types of spaces. We prove that, under some conditions, an into-isometric mapping from the unit sphere S（t（2）^∞） to S（L^1（μ） can be （real） linearly isometrically extended.
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| 关 键 词： | 等容积映射 等容积伸展 差积空间 球面单位 |
| 收稿时间： | 2004-11-08 |
| 修稿时间： | 2004-11-082005-08-24 |
The Isometric Extension of an Into Mapping from the Unit Sphere
S{\left( {{\ell }^{\infty }_{{{\left( 2 \right)}}} } \right)}
to
S{\left( {L^{1} {\left( \mu \right)}} \right)} |
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| Authors: | Guang Gui Ding |
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| Institution: | 1. School of Mathematical Science and LPMC, Nankai University, Tianjin 300071, P. R. China
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| Abstract: | This is the first paper to consider the isometric extension problem of an into–mapping between the unit spheres of two different types of spaces. We prove that, under some conditions, an into–isometric mapping from the unit sphere $ S{\left( {{\ell }^{\infty }_{{{\left( 2 \right)}}} } \right)} $ to $ S{\left( {L^{1} {\left( \mu \right)}} \right)} $ can be (real) linearly isometrically extended. |
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| Keywords: | isometric mapping isometric extension |
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