在G-M型空间上，利用其特殊的空间结构，借助以强不可约算子类为中心的具有不可约性算子类作为工具，应用算子代数K理论的语言研究算子结构，探索空间结构和算子结构二者相互影响、相互作用、相互制约的内在规律。聚焦于如下前沿问题：(1) 具有不可约性算子类的性质。(2) 具有不可约性算子类的小紧摄动问题。(3) 具有不可约性算子的直和类在全体算子集中的分布。(4) 具有不可约性算子类的相似不变量。(5)强不可约算子的直接积分。(6) G-M型空间结构的深入研究和算子代数K理论。本项目的主要特色之一是拓广为以强不可约算子类为中心的一系列具有不可约性的算子类，并以其为工具研究空间结构和算子结构。

This project researches the operator structure on the G-M type spaces by using the special structure of G-M type spaces and K-theory of operator algebras, with a variety of operators of irreducibility as tools. It explores the inherent laws of the mutual influence, interaction and the mutual restriction between the research of the structure of Banach spaces and the research of operator structure. It focuses on the following problems: (1) the properties of the classes of operators with irreducibility; (2) the small and compact perturbation problems of the classes of operators with irreducibility; (3) the distribution of the classes of operators which can be decomposed into the direct sums of finitely operators with irreducibility; (4) the similar invariants of the classes of operators with irreducibility; (5) the direct integrals of the class of strongly irreducible operators; (6) the research of the G-M type space structure and the K-theory of operator algebras. One of the main features of this project is that it expands to a series of operators with irreducibility with the class of strongly irreducible operators as the center and it uses these classes of operators as tools to study the space structure and the operator structure.