Judgement of Browder’s theorem for bounded linear operators  and their functions

QIU Sinan; CAO Xiaohong

doi:10.13471/j.cnki.acta.snus.2020A070

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Judgement of Browder’s theorem for bounded linear operators and their functions

Research articles | 更新时间：2023-11-01

- Judgement of Browder’s theorem for bounded linear operators and their functions
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 61, Issue 5, Pages: 165-172(2022)
- 作者机构：
  
  陕西师范大学数学与统计学院，陕西西安 710119
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2020A070
  CLC： O177.2
- Published：25 September 2022，
  
  Published Online：10 March 2022，
  
  Received：01 December 2020，
  
  Accepted：24 April 2021
扫描看全文
仇思楠,曹小红.有界线性算子及其函数的Browder定理的判定[J].中山大学学报(自然科学版),2022,61(05):165-172.

QIU Sinan,CAO Xiaohong.Judgement of Browder’s theorem for bounded linear operators and their functions[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(05):165-172.
仇思楠,曹小红.有界线性算子及其函数的Browder定理的判定[J].中山大学学报(自然科学版),2022,61(05):165-172. DOI： 10.13471/j.cnki.acta.snus.2020A070.

QIU Sinan,CAO Xiaohong.Judgement of Browder’s theorem for bounded linear operators and their functions[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(05):165-172. DOI： 10.13471/j.cnki.acta.snus.2020A070.

摘要

令

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2.28600001

为无限维复可分的Hilbert空间，

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49441751&type=

7.45066643

3.21733332

为

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49441773&type=

2.28600001

上的有界线性算子全体。对

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49441789&type=

13.03866673

3.21733332

，若

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49441813&type=

19.64266586

3.30200005

，称

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49441862&type=

1.94733346

2.28600001

满足Browder定理，其中

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49441835&type=

8.04333401

3.30200005

和

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7.70466709

3.30200005

分别表示算子

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1.94733346

2.28600001

的Weyl谱和Browder谱。本文借助新定义的谱集，给出了有界线性算子及其函数满足Browder定理的新的判定方法。

Abstract

Let

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2.70933342

2.62466669

be an infinite dimensional separable complex Hilbert space and

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8.72066593

3.72533321

the algebra of all bounded linear operators on

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49441985&type=

2.70933342

2.62466669

. An operator

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15.15533447

3.72533321

is said to satisfy Browder’s theorem if

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49441915&type=

22.60600090

3.72533321

， where

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49441934&type=

9.22866726

3.72533321

and

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49441939&type=

8.89000034

3.72533321

denote the Weyl spectrum and the Browder spectrum of

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49446711&type=

2.28600001

2.62466669

， respectively. With the help of a newly defined spectral set， we give new judgment methods for linear bounded operators and their functions to obey Browder’s theorem.

关键词

Browder定理谱Fredholm算子的摄动定理

Keywords

Browder’s theoremspectrumperturbation theorem of Fredholm operators

references

WEYL H V. Über beschränkte quadratische formen， deren differenz vollstetig ist ［J］. Rendiconti Del Circolo Matematico Di Palermo， 1909， 27（1）： 373-392.

BERBERIAN S K. An extension of Weyl’s theorem to a class of not necessarily normal operators ［J］. Michigan Mathematical Journal， 1969， 16（3）： 273-279.

LI C G， ZHU S， FENG Y L. Weyl’s theorem for functions of operators and approximation ［J］. Integral Equations and Operator Theory， 2010， 67（4）： 481-497.

CURTO R E， HAN Y M. Weyl’s theorem for algebraically paranormal operators ［J］. Integral Equations and Operator Theory， 2003， 47（3）： 307-314.

AN I， HAN Y. Weyl’s theorem for algebraically quasi-class A operators ［J］. Integral Equations and Operator Theory， 2008， 62（1）： 1-10.

SHI W， CAO X. Weyl’s theorem for the square of operator and perturbations ［J］. Communications in Contemporary Mathematics， 2015， 17（5）： 36-46 .

COBURN L A. Weyl’s theorem for nonnormal operators ［J］. Michigan Mathematical Journal， 1966， 13（3）： 285-288.

DUGGAL B P. The Weyl spectrum of p-hyponormal operators ［J］. Integral Equations and Operator Theory， 1997， 29（2）： 197-201.

CAO X. Analytically class operators and Weyl’s theorem ［J］. Journal of Mathematical Analysis and Applications， 2006， 320（2）： 795-803.

HARTE R， LEE W Y. Another note on Weyl’s theorem ［J］. Trans Amer Math Soc， 1997， 349（5）： 2115-2124.

CAO X， GUO M， MENG B. Weyl spectra and Weyl’s theorem ［J］. Journal of Mathematical Analysis and Applications， 2003， 288（2）： 758-767.

闫慧凰，曹小红. 有界线性算子及其函数演算的Weyl定理［J］.中山大学学报（自然科学版）， 2020， 59（2）： 22-27.

王静，曹小红. 有界线性算子的Weyl定理的判定［J］.浙江大学学报（理学版）， 2020， 47（5）： 541-547.

SCHMOEGER C. Ein Spektralabbildungs satz ［J］. Arch Math， 1990， 55（5）： 484-489.

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Related Author

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Related Institution

School of Mathematics and Statistics， Weinan Normal University

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