A Remark on Extension of Into Isometries  

作　　者：Rui Dong WANG 

机构地区：[1]School of Mathematics, Nankai University, Tianjin 300071, P. R. China [2]Department of Mathematics, Tianjin University of Technology, Tianjin 300191, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2010年第1期203-208,共6页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant No. 10871101);the Doctoral Pr0grame Foundation of Institution of Higher Education (Grant No. 20060055010)

摘　　要：In this paper, we prove that an into isometry form S（l（n）^∞） to S（E）, which under some conditions, can be extended to be a linear isometry defined on the whole space. Therefore we improve the results of [Ding, G. G.： The isometric extension of an into mapping from the unit sphere S（l（2）^∞） to S（Lμ^1）. Acta Mathematica Sinica, English Series, 22（6）, 1721-1724 （2006）].In this paper, we prove that an into isometry form S（l（n）^∞） to S（E）, which under some conditions, can be extended to be a linear isometry defined on the whole space. Therefore we improve the results of [Ding, G. G.： The isometric extension of an into mapping from the unit sphere S（l（2）^∞） to S（Lμ^1）. Acta Mathematica Sinica, English Series, 22（6）, 1721-1724 （2006）].

关 键 词：isometric extension Tingley＇s problem l（n）^∞-space 

分 类 号：O177.2[理学—数学] P413[理学—基础数学]