More on stability of almost surjective ε-isometries of Banach spaces

查看全文 作　　者：CHENG [1]LiXin;SHEN [1]QinRui;ZHANG [1]Wen;ZHOU [2]Yu

机构地区：[1]School of Mathematical Sciences, Xiamen University;[2]School of Fundamental Studies, Shanghai University of Engineering Science

出　　处：《Science China Mathematics》索引2017年第60卷第2期,共8页

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11371296, 11401370 and 11471270);Ph D Programs Foundation of Ministry of Education of the Peoples Republic of China (Grant No. 20130121110032);Natural Science Foundation of Fujian Province (Grant No. 2015J01022);Fundamental Research Funds for the Central Universities (Grant No. 20720160010) 摘　　要：Let X and Y be two Banach spaces,and f:X→Y be a standard ε-isometry for some ε >= 0.In this paper,by using a recent theorem established by Cheng et al.(2013–2015),we show a sufficient condition guaranteeing the following sharp stability inequality of f:There is a surjective linear operator T:Y→X of norm one so that ||T f(x)-x||<= 2ε,for all x∈X.As its application,we prove the following statements are equivalent for a standard ε-isometry f:X→Y:(i)lim inf_(t→∞) dist(ty,f(X))/|t|<1/2,for all y∈S_Y;(ii)τ(f)≡sup_(y∈S_Y) lim inf_(t→∞) dist(ty,f(X))/|t|=0;(iii)there is a surjective linear isometry U:X→Y so that || f(x)-Ux||<= 2ε,for all x∈X.This gives an affirmative answer to a question proposed by Vestfrid(2004,2015). 关键词：巴拿赫空间等距稳定 BANACH SHARP show NORM its

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More on stability of almost surjective ε-isometries of Banach spaces

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