一致Fredholm指标性质与(<i>ω</i><sub>1</sub>)性质

一致Fredholm指标性质与(ω₁)性质

基金项目: 国家自然科学基金(11501419); 渭南师范学院特色学科建设项目(18TSXK03); 渭南师范学院教育科学研究项目(2019JYKX018)

School of Mathematics and Statistics, Weinan Normal University, Weinan Shaanxi　714099, China

摘要: 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$(\omega_1)$性质的充要条件. 此外, 研究了hypercyclic算子(或supercyclic算子)和$(\omega_1)$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.
- $(\omega_1)$性质 /
- hypercyclic算子 /
- 一致Fredholm指标性质 /
- 谱
Abstract: 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 $(\omega_1)$. In addition, the paper explores the relationship between the property $(\omega_1)$ and hypercyclic operators (or supercyclic operators). Meanwhile, new conditions for hypercyclic operators and supercyclic operators are given.
- property $(\omega_1)$ /
- hypercyclic operator /
- property of the consistent Fredholm index /
- spectrum

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