华东师范大学学报（自然科学版） ›› 2020, Vol. 2020 ›› Issue (2): 1-7.doi: 10.3969/j.issn.1000-5641.201911004

• 数学 •    下一篇

一致Fredholm指标性质与(ω1)性质

戴磊   

  1. 渭南师范学院 数学与统计学院, 陕西 渭南　714099
  • 收稿日期:2019-01-06 发布日期:2020-03-16
  • 作者简介:戴磊,男,博士,副教授,研究方向为算子代数与算子理论.E-mail:leidai@yeah.net
  • 基金资助:
    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）

Property of the consistent Fredholm index and property (ω1)

DAI Lei   

  1. School of Mathematics and Statistics, Weinan Normal University, Weinan Shaanxi　714099, China
  • Received:2019-01-06 Published:2020-03-16

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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(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.

关键词: (ω1)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 (ω1). In addition, the paper explores the relationship between the property (ω1) and hypercyclic operators (or supercyclic operators). Meanwhile, new conditions for hypercyclic operators and supercyclic operators are given.

Key words: property (ω1), hypercyclic operator, property of the consistent Fredholm index, spectrum

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