On the Symmetrizations of ε-Isometries on Banach Spaces

被引：2
|
作者：
Cheng, Lixin [1 ]
Sun, Longfa [1 ]
机构：
[1] Xiamen Univ, Sch Math Sci, Xiamen, Fujian, Peoples R China
来源：
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS | 2019年 / 53卷 / 01期
关键词：
symmetrization of epsilon-isometry; stability; weak stability; Banach space; STABILITY;
D O I：
10.1007/s10688-019-0252-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A weak stability bound for the symmetrization T = (f(center dot) -f(-center dot))/ 2 of a general e-isometry f from a Banach space X to a Banach space Y is presented. As a corollary, the following somewhat surprising weak stability result is obtained: For every x *. X *, there exists a.. Y * with . = x * := r such that | x *, x -., T(x) | 3 2 re for all x. X. This result is used to prove new stability theorems for the symmetrization T of f
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页码：74 / 77
页数：4
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