有界线性算子及其函数的Browder定理的判定
Judgement of Browder’s theorem for bounded linear operators and their functions
- 中山大学学报(自然科学版)(中英文) 2022年61卷第5期 页码：165-172
- 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：
仇思楠（1995年生），女；研究方向：算子理论；E-mail：qiusinan111@163.com
曹小红（1972年生），女；研究方向：算子理论；E-mail：xiaohongcao@snnu.edu.cn
- 基金信息：国家自然科学基金(11471200)
DOI：10.13471/j.cnki.acta.snus.2020A070
中图分类号： O177.2纸质出版日期：2022-09-25，
网络出版日期：2022-03-10，
收稿日期：2020-12-01，
录用日期：2021-04-24
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
2.28600001
为无限维复可分的Hilbert空间，
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7.45066643
3.21733332
为
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2.28600001
2.28600001
上的有界线性算子全体。对
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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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1.94733346
2.28600001
满足Browder定理，其中
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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
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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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2.70933342
2.62466669
. An operator
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15.15533447
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is said to satisfy Browder’s theorem if
<math id="M14"><msub><mrow><mi>σ</mi></mrow><mrow><mi>w</mi></mrow></msub><mfenced separators="|"><mrow><mi>T</mi></mrow></mfenced><mo>=</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi>b</mi></mrow></msub><mfenced separators="|"><mrow><mi>T</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49441917&type=
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=49441937&type=
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9.22866726
3.72533321
and
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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
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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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