两个$l^p(\Gamma)$型空间单位球面之间的1-Lipschitz映射的延拓($1

On Extension of 1-Lipschitz Mappings between Two Unit Spheres of $ l^p(\Gamma)$ Type Spaces ($1

中文关键词:  1-Lipschitz映射  $l^p(\Gamma)$型空间  等距延拓.

英文关键词:1-Lipschitz mapping  $l^p(\Gamma)$ type space  isometric extension.

中文摘要:

      设 $T$是$l^p(\Gamma)$型空间单位球面 $S[l^p(\Gamma)]$ 到 $S[l^p(\Delta)]$ 单位球面的一个映射. 我们证明：若 T 是 1-Lipschitz 的且 $-T[S[l^p(\Gamma)]]\subset T[S[l^p(\Gamma)]]$($p > 2$), 则$T$可以延拓为全空间上的线性等距算子；若$T^{-1}$ 存在且为 1-Lipschitz的($1

英文摘要:

      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