算子代数的分类问题一直是非常重要的课题，目前对顺C*代数分类的研究已基本趋于完善，同时还衍生出许多与顺从性相关的性质，比如：Haagerup性、Kazhdan's T性、相似度等。有关C*代数顺从性的研究极大推动了C*代数、Von Neumman代数和抽象调和分析的发展。然而，目前人们对一般顺从算子代数的结构仍知之甚少，申请者近年来已对由单个算子生成的顺从算子代数的结构进行了深入研究并初步取得了一些结果。 为了更清楚、更完善的研究一般顺从算子代数的结构，本课题旨在将C*代数上与顺从性相关的性质引入到非自伴算子代数上来，并研究这类非自伴算子代数的结构，从而为最终解决是否每一个具有顺从性的算子代数都一定相似于一个C*代数的猜测、Kadison相似问题以及算子理论、算子代数中的其它经典问题提供新的思路和方法。

The classification of operator algebras is very impotent project in functional analysis,at present,the classification of amenable C*algebras tends to perfection,and at the same time,it introduces lots of amenability-related properties for C*algebras for example Haagerup property,Kazhdan's T property,similary degree,e.t. The research of amenable C*algebras drive the development of C*algebras,Von Neumman algebras and harmonic analysis mostly. However,the structure of amenable operator algebras is still less known. Recently, we have studied the structure of amenable operator algebras which is generated by an operator and got some interesting results. In order to get better understand the structure of amenable operator algebras,this project aims at extenting the concept of the amenability-related properties for C*algebras to nonselfadjoint operator algebras and studying the structure of such nonselfadjoint operator algebras. Further,it will be a great help for solving some classical problems in operator theory and operator algebras.