完全不可约算子的近期研究

总结近两年来有关完全不可约算子更深入的工作。它包括了如下几个方面：（１）完全不可约算子的谱图形和精致的完全不可约算子的存在性;（２）算子的完全不可约分解的唯一性;（３）完全不可约算子的紧扰动和（ｕ＋Ｋ）轨道。文中列出的一些结果回答了江泽坚、Ｈｅｒ－ｒｅｒｏ有关完全不可约算子的部分猜测和问题。

DevelopingWork on Completely Irreducible Operators

In 1],Z J Jiang and S L Sun sumarized the work on completely irreducible operators thathave been done by functional analysis seminar of Jilin University in the past more than ten years. Thework in1]confirmed a conjecture posed by Z J Jing in l979 "The completely irreducible operator is arather suitable analogue of Jordan block in Hilbert space.In this paper,we sum up developing work on the completely irreducible operator in recent years,it contains the following three aspects:(1)The spectral pictures of the completely irreducible opera- tor and the existence of the nice completely irreducible operator;(2)The uniqueness of the completelyirreducible decomposition of operators;(3)The perturbation and(u+K)-orbit of the completely irre-ducible operator. The results of the paper answers some conjectures and questions posed by Z J Jiang and D AHerrero.