本项目以非交换空间为主要研究对象，研究其上的Hankel算子、强不可约算子和谱理论，体现了空间理论与算子(代数)理论的互动作用。本项目聚焦于如下关键问题：.问题一、右序群上的非交换Hardy空间上的Hankel算子的有界性与紧性。.问题二、Banach空间上强不可约算子的相似不变量、交换空间与非交换空间上强不可约算子的异同点。.问题三、Banach代数上元素广义Fredholm理论、交换空间与非交换空间上算子谱理论的异同点。.本项目的创新之处在于：这是第一次在非交换空间上研究强不可约算子与谱理论。

This project takes noncommutative spaces as the main object of the research. It studies Hankel operators, strongly irreducible operators and spectral theory on them. It reflects the interaction between the space theory and the operator (algebra) theory. It focuses on the following problems: .(1) the boundedness and compactness of Hankel operators on noncommutative Hardy spaces over right ordered groups; .(2) the similarity invariants of strongly irreducible operators on Banach sapces, the similarities and differences of strongly irreducible operators on commutative spaces and noncommutative spaces; .(3) the generalized Fredholm theory of elements in Banach algebras, the similarities and differences of spectral theory on commutative spaces and noncommutative spaces. .The innovation of the project lies in: it is the first time to research strongly irreducible operators and spectral theory on noncommutative spaces.