关于保持距离相等映射和逼近满等距算子的两个注记(英文)  

Two Notes on Maps Preserving Equality of Distance and Approximate Surjective Isometries

作　　者：刘锐[1] 卢国祥[2] 

机构地区：[1]南开大学数学系和核心数学与组合数学重点实验室,天津300071 [2]中南财经政法大学统计与数学学院,湖北武汉430073

出　　处：《应用数学》2012年第4期834-838,共5页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China (11001134 , 11126250);the Fundamental Research Funds for the Central Universities;the Tianjin Science & Technology Fund (20100820)

摘　　要：在本文中,给出经典等距理论领域中的两个注记.关于FulviaSkof[1]的结果,用于赋范空间的严格凸性的研究,用Voft定理[2]给出这个著名结果的推广,并且我们的证明比原证明更短.此外,指出实Banach空间上的逼近满等距算子和有限维空间上的一般等距算子都是线性的,从而知道满射条件是本质的.In this paper, we give two notes in the field of classical isometric theory. In connection with the result of Fulvia Skof, which is useful in the study of the strict convexity of normed spaces,we give a generalization of the above known result by using Vogt＇s theorem , and the proof is shorter than the original one. Moreover, we point out that both the approximate surjective isomet- ric operators on real Banach spaces and the general isometries on finite dimensional spaces are line- ar,and it is observed by these that the surjectivity assumption is essential.

关 键 词：保持距离相等映射 δ-满等距算子 Mazur—Ulam定理 

分 类 号：O177.2[理学—数学]