On Linearly Isometric Extensions for 1-Lipschitz Mappings Between Unit Spheres of ALP-spaces (p>2)  

作　　者：Guang Gui DING 

机构地区：[1]School of Mathematical Science and LPMC, Nankai University, Tianjin 300071, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2010年第2期331-336,共6页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant No. 10871101);Research Fund for the Doctoral Program of Higher Education (Grant No. 20060055010)

摘　　要：In this paper, we show that if Vo is a 1-Lipschitz mapping between unit spheres of two ALP-spaces with p 〉 2 and -Vo（S1（LP）） C Vo（S1（LP））, then V0 can be extended to a linear isometry defined on the whole space. If 1 〈 p 〈 2 and Vo is an ＂anti-l-Lipschitz＂ mapping, then Vo can also be linearly and isometrically extended.In this paper, we show that if Vo is a 1-Lipschitz mapping between unit spheres of two ALP-spaces with p 〉 2 and -Vo（S1（LP）） C Vo（S1（LP））, then V0 can be extended to a linear isometry defined on the whole space. If 1 〈 p 〈 2 and Vo is an ＂anti-l-Lipschitz＂ mapping, then Vo can also be linearly and isometrically extended.

关 键 词：isometric extension ALp-space strictly convex 

分 类 号：O177[理学—数学] O177.2[理学—基础数学]