摘要
Banach空间的保度量(等距)映射研究自从Mazur-Ulam定理(1932)(Banach空间之间的保度量满射一定是仿射映射)开始,已经进行了80多年.本文主要对Banach空间上的保度量映射、或者等距映射及其推广形式—扰动等距和粗等距的研究历史进行回顾,同时也包含一些新的结果.本文重点放在近十年来的研究进展,以及目前该领域所关注的问题介绍.
The study of isometries of Banach spaces and their generalizations has lasted over 80 years since the celebrated Mazur-Ulam theorem(1932): Every surjective isometry between two Banach spaces is necessarily affine. This survey paper gives a historical overview of the research field. It focuses on the progress in the last ten years, especially, on the stability problems of isometries, perturbed isometries and coarse isometries defined on real Banach spaces with the special emphases on the recent developments and some open questions in this field and related topics.
出处
《中国科学：数学》
CSCD
北大核心
2020年第12期1667-1694,共28页
Scientia Sinica：Mathematica
基金
国家自然科学基金(批准号:11731010)资助项目。
