The property （<italic style="font-style: italic">R</italic><sub>1</sub>） and its perturbations for bounded linear operators

ZHAO Xiaopeng; DAI Lei; CAO Xiaohong

doi:10.13471/j.cnki.acta.snus.2021A005

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The property （R₁） and its perturbations for bounded linear operators

Research articles | 更新时间：2023-11-01

- The property （R₁） and its perturbations for bounded linear operators
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 61, Issue 6, Pages: 172-179(2022)
- 作者机构：
  
  1.渭南师范学院数学与统计学院，陕西渭南 714099
  2.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.2021A005
  CLC： O177.2
- Published：25 November 2022，
  
  Published Online：28 July 2022，
  
  Received：15 January 2021，
  
  Accepted：02 September 2021
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赵小鹏,戴磊,曹小红.有界线性算子的（R₁）性质及其摄动[J].中山大学学报(自然科学版),2022,61(06):172-179.

ZHAO Xiaopeng,DAI Lei,CAO Xiaohong.The property （R₁） and its perturbations for bounded linear operators[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(06):172-179.
赵小鹏,戴磊,曹小红.有界线性算子的（R₁）性质及其摄动[J].中山大学学报(自然科学版),2022,61(06):172-179. DOI： 10.13471/j.cnki.acta.snus.2021A005.

ZHAO Xiaopeng,DAI Lei,CAO Xiaohong.The property （R₁） and its perturbations for bounded linear operators[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(06):172-179. DOI： 10.13471/j.cnki.acta.snus.2021A005.

摘要

利用拓扑一致降标诱导的谱集，给出了算子

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435500&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435499&type=

2.28600001

2.62466669

及算子函数

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435493&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435503&type=

6.85799980

3.55599999

有

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435495&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435509&type=

5.58799982

3.89466691

性质的等价性刻画。另外，上三角算子矩阵的

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435564&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435549&type=

5.58799982

3.89466691

性质的稳定性得到了研究。

Abstract

Using the spectrum introduced by the property of topological uniform descent， we give the necessary and sufficient conditions for which the property

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435533&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435518&type=

6.43466663

4.57200003

holds for bounded linear operators

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435525&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435535&type=

2.28600001

2.62466669

and operator functions

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435540&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435538&type=

6.85799980

3.55599999

. In addition， the perturbations of property

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435589&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435570&type=

6.43466663

4.57200003

for upper triangular operator matrices is considered.

关键词

拓扑一致降标<math id="M9"><mo stretchy="false">(</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435564&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435549&type=5.587999823.89466691性质谱

Keywords

topological uniform descentproperty<math id="M10"><mtext> </mtext><mo stretchy="false">(</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">)</mo></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435566&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49435556&type=7.196666244.57200003spectrum

references

WEYL H V. Über beschränkte quadratische formen， deren differenz vollstetig ist ［J］. Rend Circ Mat Palermo， 1909， 27（1）： 373-392.

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

RAKOCEVIC V. Operators obeying a-Weyl's theorem ［J］. Rev Roumaine Math Pures Appl， 1986， 34（10）： 915-919.

RAKOCEVIC V. On a class of operators ［J］. Mat Vesnik， 1985， 37（92）： 423-425.

AIENA P， GUILLÉN J R， PEÑA P. Property <math id="M581"><mo stretchy="false">(</mo><mi>R</mi><mo stretchy="false">)</mo></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49438610&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49438609&type=4.487333302.96333337 for bounded linear operators ［J］. Mediterr J Math， 2011， 8（4）： 491-508.

AIENA P， APONTE E， GUILLÉN J R，et al. Property <math id="M582"><mo stretchy="false">(</mo><mi>R</mi><mo stretchy="false">)</mo></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49438610&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49438609&type=4.487333302.96333337 under perturbations ［J］. Mediterr J Math， 2013， 10（1）： 367-382.

JIA B T， FENG Y L. Property <math id="M583"><mo stretchy="false">(</mo><mi>R</mi><mo stretchy="false">)</mo></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49438610&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49438609&type=4.487333302.96333337 under compact perturbations ［J］. Mediterr J Math， 2020， 17（2）：73.

赵小鹏, 戴磊, 曹小红. 有界线性算子的拓扑一致降标与(R)性质［J］. 山东大学学报(理学版), 2021, 56(12): 59-66.

GRABINER S. Uniform ascent and descent of bounded operators ［J］. J Math Soc Japan， 1982， 34（2）： 317-337.

DONG J， CAO X H. Compact perturbations of both SVEP and Weyl's theorem for 3×3 upper triangular operator matrices［J］. Linear Multilinear Algebra， 2020， 68（10）： 2020-2033.

DONG J， CAO X H. The （generalized） Weylness of upper triangular operator matrices ［J］. Anal Math，2020，46（3）：465-481.

CUI M M， CAO X H. Weyl's theorem for upper triangular operator matrix and perturbations ［J］. Linear Multilinear Algebra， 2018，66（7）： 1299-1310.

吴学俪，曹小红，张敏. 上三角算子矩阵的（ω）性质的摄动［J］. 西北大学学报（自然科学版），2017， 47（2）：167-173.

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.

CAO X H， GUO M Z. MENG B. Semi-Fredholm spectrum and Weyl's theorem for operator matrices ［J］. Acta Math Sin （Engl Ser）， 2006， 22（1）： 169-178.

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The property （R1） and its perturbations for bounded linear operators

DOI：10.13471/j.cnki.acta.snus.2021A005

摘要

Abstract

关键词

Keywords

references

The property （R₁） and its perturbations for bounded linear operators