经典Banach空间嵌入理论一直是泛函分析研究的核心问题。近十年来，具有深刻粗几何背景的"粗嵌入"成为"嵌入"研究领域中目前国际同行高度关注的一个崭新课题。本项目致力于加强和发展嵌入问题研究的理论、工具和方法，将经典"嵌入"理论和现代的"粗嵌入"理论有机结合起来，探讨和解决或部分解决下列领域的重要问题： （1）Banach空间上的扰动等距与等距嵌入； （2）度量空间上的扰动等距与粗等距的逼近； （3）超弱紧集向超自反空间的嵌入问题； （4）有界几何度量空间可嵌入进超自反、Hilbert空间和具有"性质H"的Banach空间的特征和充分条件； （5）具有"性质H"的Banach空间的特征。

The classical embedding theory of Banach spaces has always been an important problem in the study of functional analysis. In recent ten years, the "coarse embedding" of the profound background of coarse geometry has become a very new topic in the embedding research field and it has been received great concern.The purpose of the projection is to strength and develop the theory,tools and methods in the embedding research field. Combining the classical "embedding" with the modern "coarse embedding",we want to solve or partly solve some important problems in the following fields: (1)the perturbations of isometries on Banach spaces and isometric embedding; (2)the perturbations of isometries on metric spaces and the approximations of coarse isometries; (3)the embeddings of super weakly compact sets into super reflexive Banach spaces; (4)the embedding characterizations and sufficient conditions of bound geometric metric spaces into super reflexive, Hilbert spaces and those spaces with "Property H"; (5)the characterizations of Banach spaces with "Property H."