一致Fredholm指标性质与(ω^1)性质

Property of the consistent Fredholm index and property (ω^1)

根据一致Fredholm指标性质定义了一种新的谱集,利用该谱集给出了Hilbert空间中有界线性算子满足(ω1)性质的充要条件.此外,研究了hypercyclic算子(或supercyclic算子)和(ω1)性质之间的关系,同时给出了hypercyclic算子与supercyclic算子新的判定方法.

In this paper,a new spectrum is defined according to the property of the consistent Fredholm index.We establish the sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space that satisfies the property(ω1).In addition,the paper explores the relationship between the property(ω1)hypercyclic operators and supercyclic operators are given.