| 两个$l^p(Gamma)$型空间单位球面之间的1-Lipschitz映射的延拓($1 |
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| 引用本文： | 方习年. 两个$l^p(Gamma)$型空间单位球面之间的1-Lipschitz映射的延拓($1
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| 作者姓名： | 方习年 |
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| 作者单位： | 南京审计学院应用数学系, 江苏 南京 210029 |
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| 基金项目： | 江苏省教育厅自然科学基金(No.06KJD110092). |
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| 摘 要： | Let T be a mapping from the unit sphere S[l^p（Г）] into S[l^p（△）] of two atomic AL^p- spaces. We prove that if T is a 1-Lipschitz mapping such that -T[S[l^p（Г）]] belong to T[S[l^p（Г）]], then T can be linearly isometrically extended to the whole space for p 〉 2; if T is injective and the inverse mapping T^-1 is a 1-Lipschitz mapping, then T can be extended to be a linear isometry from l^p（Г） into l^p（△） for 1 〈 p ≤ 2.
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| 关 键 词： | Lipschitz映射 单位球面 名称 空间 线性等距 逆映射 原子 磷 |
| 收稿时间： | 2007-05-18 |
| 修稿时间： | 2008-04-22 |
On Extension of 1-Lipschitz Mappings between Two Unit Spheres of $ l^p(Gamma)$ Type Spaces ($1 |
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| FANG Xi Nian. On Extension of 1-Lipschitz Mappings between Two Unit Spheres of $ l^p(Gamma)$ Type Spaces ($1
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| Authors: | FANG Xi Nian |
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| Affiliation: | Department of Applied Mathematics, Audit University, Jiangsu 210029, China |
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| Abstract: | Let $T$ be a mapping from the unit sphere $S[l^p(Gamma)]$ into $S[l^p(Delta)]$ of two atomic $AL^p$-spaces. We prove that if $T$ is a 1-Lipschitz mapping such that $-T[S[l^p(Gamma)]]subset T[S[l^p(Gamma)]]$, then $T$ can be linearly isometrically extended to the whole space for $p>2$; if $T$ is injective and the inverse mapping $T^{-1}$ is a 1-Lipschitz mapping, then $T$ can be extended to be a linear isometry from $l^p(Gamma)$ into $l^p(triangle)$ for $1
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| Keywords: | 1-Lipschitz mapping $l^p(Gamma)$ type space isometric extension. |
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