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 linear...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.展开更多
基金the Natural Science Foundation of the Education Department of Jiangsu Province (No.06KJD110092)
文摘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.
