| On Extension of 1-Lipschitz Mappings between Two Unit Spheres of $ l^p(\Gamma)$ Type Spaces ($1 |
| Received:May 18, 2007 Revised:April 22, 2008 |
| Key Words:
1-Lipschitz mapping $l^p(\Gamma)$ type space isometric extension.
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| Fund Project:the Natural Science Foundation of the Education Department of Jiangsu Province (No.06KJD110092). |
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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 |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2009.04.014 |
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