自反算子代数的逆极限方法及数值域

自反算子代数是非自伴算子代数理论的核心研究内容，具有重要的理论价值和广泛的应用价值. 它们在非自伴算子代数研究中所起的作用犹如von Neumann代数在自伴代数研究中所起的作用. 近来我们发现任一自反算子代数都是具有有限不变子空间的自反算子代数的逆极限. 本项目将利用这一发现，从新的视角研究自反算子代数中逆算子连通性问题和张量积问题；同时还将研究自反算子代数中数值半径等距问题以及Lie结构和数值域的关系.

Reflexive operator algebras are the main content in the non-selfadjoint operator algebra theory, and have the important theoretical value and the applied value. They play a role in the study of non-selfadjoint operator algebras as important as von Neumann algebras do in the study of selfadjoit operator algebras. Recently, we found the fact that a reflexive operator algebra is the inverse limit of a system of reflexive algebas with finite invariant subspaces. In this project, we will use such fact to investigative the connectedness of invertible operators and tensor of reflexive algebras. Also, we will study numerical radius isometries of reflexive algebras and the relation between the Lie stuture and the numerical range.