(ω_1)性质与单值扩张性质

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英文篇名：Property (ω_1) and the single-valued extension property 作者：戴磊 ; 黄小静 ; 郭奇 英文作者：DAI Lei;HUANG Xiao-jing;GUO Qi;School of Mathematics and Physics, Weinan Normal University;School of Mathematics and Information Science, Shaanxi Normal University; 关键词：(ω_1)性质 ; 单值扩张性质 ; 亚循环算子 ; 超循环算子 ; 谱 英文关键词：property(ω_1);;single-valued extension property;;hypercyclic operator;;supercyclic operator;;spectrum 中文刊名：SDDX 英文刊名：Journal of Shandong University(Natural Science) 机构：渭南师范学院数理学院;陕西师范大学数学与信息科学学院; 出版日期：2019-05-27 10:31 出版单位：山东大学学报(理学版) 年：2019 期：v.54 基金：国家自然科学基金资助项目(11501419);; 渭南师范学院特色学科建设项目(18TSXK03) 语种：中文; 页：SDDX201908007 页数：8 CN：08 ISSN：37-1389/N 分类号：59-65+79

摘要

称有界线性算子T满足(ω_1)性质,如果T的上半Weyl谱在它的逼近点谱中的补集包含在它的谱集中孤立的有限重的特征值的全体中。根据单值扩张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(ω_1)性质的充分必要条件。作为应用,给出了亚(或超)循环算子类满足(ω_1)性质的等价刻画。
        A bounded linear operator T satisfies property(ω_1), if the complement in the approximate point spectrum σ_a(T) of the upper semi-Weyl spectrum σ_(ea)(T) is contained in the set of all isolated points of the spectrum σ(T) which are finite eigenvalues. In this paper, by means of the new spectrum defined in view of the single-valued extension property, the sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space satisfying the property(ω_1) are established. As an application, the property(ω_1) for hypercyclic(or supercyclic) operators are characterised.

引文

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