STABILITY OF A PAIR OF BANACH SPACES FOR ε-ISOMETRIES  

作　　者：Duanxu DAI Bentuo ZHENG 戴端旭;郑本拓(College of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China;Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA)

机构地区：[1]College of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China [2]Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA

出　　处：《Acta Mathematica Scientia》2019年第4期1163-1172,共10页数学物理学报（B辑英文版）

基　　金：supported in part by NSFC(11601264,11471270 and 11471271);the Fundamental Research Funds for the Central Universities(20720160037);the Outstanding Youth Scientific Research Personnel Training Program of Fujian Province;the High level Talents Innovation and Entrepreneurship Project of Quanzhou City(2017Z032);the Research Foundation of Quanzhou Normal University(2016YYKJ12);the Natural Science Foundation of Fujian Province of China(2019J05103);supported in part by NSFC(11628102)

摘　　要：A pair of Banach spaces (X, Y) is said to be stable if for every ￡-isometry f : X→Y,there exist γ> 0 and a bounded linear operator T : L(f)→X with ||T||≤α such that ||Tf(x)- x||≤γε for all x ∈ X, where L(f) is the closed linear span of f(X). In this article, we study the stability of a pair of Banach spaces (X, Y) when X is a C(K) space. This gives a new positive answer to Qian's problem. Finally, we also obtain a nonlinear version for Qian's problem.A pair of Banach spaces(X, Y) is said to be stable if for every ε-isometry f :X → Y, there exist γ > 0 and a bounded linear operator T : L(f) → X with ||T|| ≤ α such that ||T f(x)-x|| ≤ γε for all x ∈ X, where L(f) is the closed linear span of f(X). In this article, we study the stability of a pair of Banach spaces(X, Y) when X is a C(K) space.This gives a new positive answer to Qian’s problem. Finally, we also obtain a nonlinear version for Qian’s problem.

关 键 词：STABILITY ε-isometry Figiel THEOREM BANACH space 

分 类 号：O177.2[理学—数学]