(h)性质及其扰动

数学物理学报 ›› 2019, Vol. 39 ›› Issue (4): 713-719.

(h)性质及其扰动

乌日柴胡^1,²(),阿拉坦仓^3,*()

¹ 内蒙古师范大学数学科学学院呼和浩特 010022
² 内蒙古大学数学科学学院呼和浩特 010021
³ 呼和浩特民族学院数学系呼和浩特 010051

收稿日期:2018-02-09 出版日期:2019-08-26 发布日期:2019-09-11
通讯作者: 阿拉坦仓 E-mail:wurichaihu19@163.com;alatanca@imu.edu.cn
作者简介:乌日柴胡, E-mail:wurichaihu19@163.com
基金资助:
国家自然科学基金(11561053);国家自然科学基金(11761029);内蒙古自然科学基金(2018BS01001);内蒙古自治区高等学校科学研究项目(NJZZ18018);内蒙古自治区高等学校科学研究项目(NJZY18021)

Property (h) and Perturbations

Wurichaihu^1,²(), Alatancang^3,*()

¹ School of Mathematical Sciences, Inner Mongolia Normal University, Hohhot 010022
² School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021
³ Hohhot University for Nationalities, Hohhot 010051

Received:2018-02-09 Online:2019-08-26 Published:2019-09-11
Contact: Alatancang E-mail:wurichaihu19@163.com;alatanca@imu.edu.cn
Supported by:
the NSFC(11561053);the NSFC(11761029);the Natural Science Foundation of Inner Mongolia(2018BS01001);the Research Program of Sciences at Universities of Inner Mongolia Autonomous Region(NJZZ18018);the Research Program of Sciences at Universities of Inner Mongolia Autonomous Region(NJZY18021)

摘要/Abstract

摘要：

该文引入并研究了Banach空间中的有界线性算子的（h）性质，它是a-Weyl定理的推广.进而得到了（h）性质在有限秩和幂零扰动下的稳定性.单值扩张性是局部谱理论中的重要部分，该文还证明了（h）性质与单值扩张性之间的关系，从而得到了满足（h）性质的几类算子.

关键词: 单值扩张性, a-Weyl定理, (h)性质

Abstract:

In this paper, we introduce and study the property (h), which extends a-Weyl's theorem. We consider its stability under commuting finite rank and nilpotent perturbations. We prove that property (h) on Banach spaces is related to an important property which has a leading role in local spectral theory:the single-valued extension property. From this result we deduce that property (h) holds for several classes of operators.

Key words: Single-valued extension property, a-Weyl's theorem, Property (h)

中图分类号:

O177.1

乌日柴胡,阿拉坦仓. (h)性质及其扰动[J]. 数学物理学报, 2019, 39(4): 713-719.

Wurichaihu, Alatancang. Property (h) and Perturbations[J]. Acta mathematica scientia,Series A, 2019, 39(4): 713-719.

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