COARSE ISOMETRIES BETWEEN FINITE DIMENSIONAL BANACH SPACES  

作　　者：Yuqi SUN Wen ZHANG 孙玉奇;张文(School of Mathematical Science,Xiamen University,Xiamen 361005,China)

机构地区：[1]School of Mathematical Science,Xiamen University,Xiamen 361005,China

出　　处：《Acta Mathematica Scientia》2021年第5期1493-1502,共10页数学物理学报（B辑英文版）

基　　金：Supported by National Natural Science Foundation of China(11731010 and 12071388)。

摘　　要：Assume that X and Y are real Banach spaces with the same finite dimension.In this paper we show that if a standard coarse isometry f:X→Y satisfies an integral convergence condition or weak stability on a basis,then there exists a surjective linear isometry U:X→Y such that∥f(x)−Ux∥=o(∥x∥)as∥x∥→∞.This is a generalization about the result of Lindenstrauss and Szankowski on the same finite dimensional Banach spaces without the assumption of surjectivity.As a consequence,we also obtain a stability result forε-isometries which was established by Dilworth.

关 键 词：coarse isometry linear isometry finite dimensional Banach spaces 

分 类 号：O177.2[理学—数学]