Cowen-Douglas 算子与算子权移位是算子理论中两类重要的特殊算子类，二者之间有密切的联系. 关于这两类算子的研究将对探索线性算子的结构及其应用产生积极的作用，同时也将促进算子理论与代数、几何、拓扑等其它领域的交叉和融合. 本项目主要研究Cowen-Douglas算子和算子权移位的关系及它们的若干性质. 拟研究Cowen-Douglas算子何时成为加权移位（包括正交基和Schauder基的情形）；Cowen-Douglas算子与算子权移位的自反性； Cowen-Douglas算子的动力性质. 此外，研究无穷有向树上的加权移位算子等问题，期望提出新的研究课题. 本项目的特色在于将这两类算子统一考虑，以起到互相促进、互相补充的作用.

The Cowen-Douglas operators and operator weighted shifts are two important special operator classes, and there are many close relations between them. The studies for this two operator classes will bring about a positive role in exploring the structure of linear operators and their applications. Meanwhile, these studies will also promote the intersects and mixtures of operator theory and algebra, geometry and topology. This project will be mainly devoted to study the relations of Cowen-Douglas operators with operator weighted shifts and their some properties. We will consider when a Cowen-Douglas operator is a weighted shift on some orthogonal basis and some Schauder basis respectively, and reflexivity of Cowen-Douglas operators and operator weighted shifts respectively, and dynamical properties Cowen-Douglas operators. Moreover, we will discuss some subjects from weighted shifts on infinite directed trees，and expect to put forward some new research subjects. The feature of this project lie in a united consideration of Cowen-Douglas operators and operator weighted shifts, so that to produce a promotion and complement each other.