保持算子各类乘积边缘谱的一般映射的刻画

The purpose of the project is to study the structure of general maps on operator leaving the peripheral spectrum invariant of generalized product, general Jordan product and Lie product of operators on operator algebras. General preserver problems is to study the maps leaving some properties of elements in algebras invariant. Often, the characterizations of such preservers imply that they are algebric isomorphisms or algebric anti-isomorphisms, and therefore reveal the connection between the inherent properties of operator algebras and maps on itself. This makes one know and understand operator algebras more deeply. The purpose of studying general preserver problems is to seek the rigid invariant of isomorphisms, provide information of the whole structure of operator algebras and classification of operator algebras from a new angle.

本申请项目属于算子代数上一般保持问题的研究课题，主要研究算子代数上以算子广义乘积、广义Jordan乘积以及Lie积的边缘谱作为不变量的一般映射的结构性质。算子代数上的一般保持问题是研究保持算子代数中元素的某种特征不变的映射。其研究结果表明，在许多情形下，这样的映射是代数同态或代数反同态，从而揭示了算子代数的固有性质以及与其上映射的联系，使人们进一步加深对算子代数的认识和理解。一般保持问题研究的目的是寻求同构的刚性不变量，从新的角度提供算子代数的整体结构和对算子代数分类的信息。