Banach 代数上amenability 的概念最早是由 Johnson 提出的。2005 年Farenick等人将amenability 的概念引入到有界线性算子上来。此后，算子及算子代数的amenable 性引起了许多学者的关注。尤其是最近几年，这方面出现了大量的研究结果，极大地推动了算子理论及算子代数的发展。然而，目前人们对 amenable算子、算子代数的结构仍知之甚少。 因此，研究这种算子、算子代数的结构是一个很有意义的课题。如果搞清楚这类算子及算子代数的结构，将会为算子理论的许多经典问题提供一些可借鉴的思想和方法。该课题主要有两方面的内容：1. 从经典的算子理论和算子代数两个不同的角度入手来研究这类算子及算子代数的基本结构和性质（包括谱论、约化性、稳定性、换位代数等）。2. Amenable性在算子理论经典问题中的应用(例如，它与不变子空间等问题深层次的联系)。

The concept of amenability of Banach algebra was introduced firstly by Johnson. Since Farenick.et.developed this concept for bounded linear operator in 2005, lots of scholars have started to study the amenability of special operators and operator algebras.Especially in recent years, there are lots of results in this field, which drive the development of operator theory and operator algebra mostly. However, the structure of amenable operators and operator algebras is still less known. Therefore, it is an interesting problem to study the structure of amenable operators and operator algebras. If this problem is solved mostly, it will be a great help for solving some classical problems in operator theory. This problem mainly includes two parts: I: Start from the classical operator theory and operator algebra two different views to study the basic structure and properties(spectrum theory、reducible property、stability、commutant algebras.et.) of this kind of operator and operator algebra; II: The application to some classical problems in operator theory(such as，the deep link between the problems of invariant subspaces and it).