本项目属于算子理论、算子代数与量子信息理论交叉课题。主要研究与算子代数Lie结构相关的一般保持问题，包括任意von Neumann代数、Banach空间套代数等算子代数上Lie可乘同构的刻画，以Lie乘积的数值域、数值半径、谱、拟谱、谱半径等作为不变量的一般映射的结构性质，从新的角度获得对于算子代数Lie结构的新认识；同时把算子理论、算子代数以及一般保持问题研究的理论和方法应用于量子信息论，探讨连续变量系统中高斯态的纠缠刻画问题，寻求新的适宜于两体和多体连续系统的一些易于操作的纠缠判据，并探求新的量子态EPR操控性判据等。

The purpose of the project is to study the general preserver problems concerning Lie structure of operator algebras and the applications to quantum information science. The project is mainly devoted to characterizing Lie multiplicative isomorphisms and the structure of general maps on operators leaving the numerical range, the numerical radius, the spectrum, the pseudo spectrum or spectral radius invariant of Lie product of operators on operator algebras, such as the von Neumann algebras and the nest algebras on Banach spaces. This will help us to obtain some Lie structural properties of operator algebras from new aspects. Then the theory and the approaches of operator theory, operator algebras and general preserver problems will be used to study some topics in quantum information science such as characterizing the entanglement of Gaussian states in continuous multipartite systems and EPR steering criterion of quantum states.