- 个人中心
- 退出登录
浏览全部资源
扫码关注微信
- Author Center
- Manuscript Submission
- Criteria for Publicati
- Copyright Transfer
- Article Template
- Articles & Issues
- First online articles
- Latest Issue
- Archive
Property
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 64, Issue 5, Pages: 137-145(2025)
- 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.ZR20250027
CLC： O177.2Received：11 February 2025，
Revised：2025-03-18，
Accepted：31 March 2025，
Published Online：16 June 2025，
Published：25 September 2025
- 稿件说明：
移动端阅览
孙晨辉,曹小红.有界线性算子的R性质及其稳定性[J].中山大学学报(自然科学版)(中英文),2025,64(05):137-145.
SUN Chenhui ,CAO Xiaohong .Property (R) and its stability for bounded linear operator[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(05):137-145.
孙晨辉,曹小红.有界线性算子的R性质及其稳定性[J].中山大学学报(自然科学版)(中英文),2025,64(05):137-145. DOI： 10.13471/j.cnki.acta.snus.ZR20250027.
SUN Chenhui ,CAO Xiaohong .Property (R) and its stability for bounded linear operator[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(05):137-145. DOI： 10.13471/j.cnki.acta.snus.ZR20250027.
![PDF Download](/rc-pub/front/front-article/download/109628125/lowqualitypdf/Property <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mo stretchy="false">(</mo><mi>R</mi><mo stretchy="false">)</mo></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/74BC227E-D204-490e-80CF-A06ADF71394D-M002.jpg"><?fx-imagestate width="7.02733374" height="4.57200003"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/74BC227E-D204-490e-80CF-A06ADF71394D-M002c.jpg"><?fx-imagestate width="7.02733374" height="4.57200003"?></graphic></alternatives></inline-formula> and its stability for bounded linear operator.pdf){kind=link}
摘要
设
<math id="M3"><mi mathvariant="normal">H</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003365&type=
2.28600001
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003358&type=
2.28600001
为无限维复Hilbert空间，
<math id="M4"><mi>B</mi><mfenced separators="|"><mrow><mi mathvariant="normal">H</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003368&type=
3.21733332
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003383&type=
7.19666624
为
<math id="M5"><mi mathvariant="normal">H</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003365&type=
2.28600001
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003358&type=
2.28600001
上的有界线性算子的全体. 算子
<math id="M6"><mi>T</mi><mo>∈</mo><mi>B</mi><mfenced separators="|"><mrow><mi mathvariant="normal">H</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003385&type=
3.21733332
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003395&type=
12.78466606
称为具有
<math id="M7"><mfenced separators="|"><mrow><mi>R</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003376&type=
3.21733332
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003399&type=
4.57200003
性质，若
<math id="M8"><msub><mrow><mi>σ</mi></mrow><mrow><mi>a</mi></mrow></msub><mfenced separators="|"><mrow><mi>T</mi></mrow></mfenced><mo>∖</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi>a</mi><mi>b</mi></mrow></msub><mfenced separators="|"><mrow><mi>T</mi></mrow></mfenced><mo>=</mo><msub><mrow><mi>π</mi></mrow><mrow><mn mathvariant="normal">00</mn></mrow></msub><mfenced separators="|"><mrow><mi>T</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003400&type=
3.21733332
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003413&type=
31.75000000
，其中
<math id="M9"><msub><mrow><mi>σ</mi></mrow><mrow><mi>a</mi></mrow></msub><mfenced separators="|"><mrow><mi>T</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003428&type=
3.21733332
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003417&type=
7.78933382
和
<math id="M10"><msub><mrow><mi>σ</mi></mrow><mrow><mi>a</mi><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=91003439&type=
3.21733332
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003422&type=
8.55133343
分别表示算子
<math id="M11"><mi>T</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003444&type=
2.28600001
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003456&type=
1.94733346
的逼近点谱和Browder本质逼近点谱，
<math id="M12"><msub><mrow><mi>π</mi></mrow><mrow><mn mathvariant="normal">00</mn></mrow></msub><mfenced separators="|"><mrow><mi>T</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003458&type=
3.21733332
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003475&type=
8.72066593
表示谱集中孤立的有限重特征值的全体. 利用算子的一致Fredholm 非负指标性质，首先给出了有界线性算子具有
<math id="M13"><mfenced separators="|"><mrow><mi>R</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003376&type=
3.21733332
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003399&type=
4.57200003
性质的充要条件；其次讨论了
<math id="M14"><mfenced separators="|"><mrow><mi>R</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003376&type=
3.21733332
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003399&type=
4.57200003
性质的摄动. 结合算子的一致Fredholm 非负指标的特征，得到了判定算子函数具有
<math id="M15"><mfenced separators="|"><mrow><mi>R</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003376&type=
3.21733332
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003399&type=
4.57200003
性质的新途径，并揭示了
<math id="M16"><mfenced separators="|"><mrow><mi>R</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003376&type=
3.21733332
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003399&type=
4.57200003
性质的稳定性与算子函数满足
<math id="M17"><mfenced separators="|"><mrow><mi>R</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003376&type=
3.21733332
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003399&type=
4.57200003
性质的内在联系.
Abstract
Let
<math id="M18"><mi mathvariant="normal">H</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003460&type=
2.62466669
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003483&type=
2.70933342
be a complex infinite dimensional Hilbert space and
<math id="M19"><mi>B</mi><mfenced separators="|"><mrow><mi mathvariant="normal">H</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003481&type=
3.80999994
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003488&type=
8.38199997
be the algebra of all bounded linear operators from
<math id="M20"><mi mathvariant="normal">H</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003460&type=
2.62466669
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003483&type=
2.70933342
to
<math id="M21"><mi mathvariant="normal">H</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003460&type=
2.62466669
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003483&type=
2.70933342
. For
<math id="M22"><mi>T</mi><mo>∈</mo><mi>B</mi><mfenced separators="|"><mrow><mi mathvariant="normal">H</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003490&type=
3.80999994
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003492&type=
14.90133286
，
<math id="M23"><mi>T</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003504&type=
2.62466669
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003518&type=
2.28600001
is said to satisfy property
<math id="M24"><mfenced separators="|"><mrow><mi>R</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003520&type=
3.72533321
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003528&type=
5.24933338
， if
<math id="M25"><msub><mrow><mi>σ</mi></mrow><mrow><mi>a</mi></mrow></msub><mfenced separators="|"><mrow><mi>T</mi></mrow></mfenced><mo>∖</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi>a</mi><mi>b</mi></mrow></msub><mfenced separators="|"><mrow><mi>T</mi></mrow></mfenced><mo>=</mo><msub><mrow><mi>π</mi></mrow><mrow><mn mathvariant="normal">00</mn></mrow></msub><mfenced separators="|"><mrow><mi>T</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003511&type=
3.72533321
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003512&type=
36.83000183
， where
<math id="M26"><msub><mrow><mi>σ</mi></mrow><mrow><mi>a</mi></mrow></msub><mfenced separators="|"><mrow><mi>T</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003544&type=
3.72533321
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003546&type=
9.05933285
is the approximate point spectrum of
<math id="M27"><mi>T</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003504&type=
2.62466669
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003518&type=
2.28600001
，
<math id="M28"><msub><mrow><mi>σ</mi></mrow><mrow><mi>a</mi><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=91003535&type=
3.72533321
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003537&type=
9.90600014
is the Browder essential approximate point spectrum of
<math id="M29"><mi>T</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003504&type=
2.62466669
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003518&type=
2.28600001
and
<math id="M30"><msub><mrow><mi>π</mi></mrow><mrow><mn mathvariant="normal">00</mn></mrow></msub><mfenced separators="|"><mrow><mi>T</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003564&type=
3.72533321
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003566&type=
10.07533360
denotes the isolates points of the spectrum which are eigenvalues of finite multiplicity. By using the consistent Fredholm non negative index property of operators， the necessary and sufficient conditions of property
<math id="M31"><mfenced separators="|"><mrow><mi>R</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003520&type=
3.72533321
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003528&type=
5.24933338
for bounded linear operators are given. Then the stability of property
<math id="M32"><mfenced separators="|"><mrow><mi>R</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003520&type=
3.72533321
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003528&type=
5.24933338
are studied. Based on the consistent Fredholm non negative index property of operators， the new judgement method of property
<math id="M33"><mfenced separators="|"><mrow><mi>R</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003520&type=
3.72533321
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003528&type=
5.24933338
for operator function is obtained. In addition， the relationship between the stability of property
<math id="M34"><mfenced separators="|"><mrow><mi>R</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003520&type=
3.72533321
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003528&type=
5.24933338
a
nd property
<math id="M35"><mfenced separators="|"><mrow><mi>R</mi></mrow></mfenced></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003520&type=
3.72533321
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91003528&type=
5.24933338
for operator function is revealed.
关键词
Keywords
references
AIENA P ， TRIOLO S ， 2018 . Weyl-type theorems on Banach spaces under compact perturbations ［J］. Mediterr J Math ， 15 （ 3 ）： 126 .
BERKANI M ， KACHAD M ， 2015 . New Browder and Weyl type theorems ［J］. Bull Korean Math Soc ， 52 （ 2 ）： 439 - 452 .
CAO X H ， 2008 . Weyl spectrum of the products of operators ［J］. J Korean Math Soc ， 45 （ 3 ）： 771 - 780 .
CAO X H ， GUO M Z ， MENG B ， 2003 . Weyl spectra and Weyl's theorem ［J］. J Math Anal Appl ， 288 （ 2 ）： 758 - 767 .
DJORDJEVIĆ D S ， 1999 . Operators obeying a -Weyl's theorem ［J］. Publ Math Debrecen ， 55 （ 3/4 ）： 283 - 298 .
DONG J ， CAO X H ， 2020 . Compact perturbations of both SVEP and Weyl's theorem for <math id="M729"><mn mathvariant="normal">3</mn><mo>×</mo><mn mathvariant="normal">3</mn></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91006157&type= 2.28600001 https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91006132&type= 7.11199999 upper triangular operator matrices ［J］. Linear Multilinear A ， 68 （ 10 ）： 2020 - 2033 .
GUPTA A ， KUMAR A ， 2020 . Properties （BR） and （BgR） for bounded linear operators ［J］. Rend Del Circolo Matematico Di Palermo Ser 2 ， 69 （ 2 ）： 601 - 611 .
JIA B T ， FENG Y L ， 2020 . Property <math id="M730"><mfenced separators="|"><mrow><mi>R</mi></mrow></mfenced></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91006158&type= 3.21733332 https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91006134&type= 4.57200003 under compact perturbations ［J］. Mediterr J Math ， 17 （ 2 ）： 73 .
SUN C H ， CAO X H ， 2022 . Criteria for the property （UWE） and the a-Weyl theorem ［J］. Funct Anal Appl ， 56 （ 3 ）： 216 - 224 .
WU X F ， HUANG J J ， CHEN A ， 2018 . Weylness of 2×2 operator matrices ［J］. Math Nachr ， 291 （ 1 ）： 187 - 203 .
YANG L L ， CAO X H ， 2023 . Perturbations of spectra and property <math id="M731"><mfenced separators="|"><mrow><mi>R</mi></mrow></mfenced></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91006158&type= 3.21733332 https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=91006134&type= 4.57200003 for upper triangular operator matrices ［J］. J Math Anal Appl ， 519 （ 1 ）： 126797 .
ZHU S ， LI C G ， ZHOU T T ， 2012 . Weyl type theorems for functions of operators ［J］. Glasgow Math J ， 54 （ 3 ）： 493 - 505 .
0
Views
94
下载量
0
CSCD
- L-PDFDownload
- Meta-XMLDownload
- BibTeXDownload
- EndnoteDownload
- RefMan Download
- NoteExpressDownload
- NoteFirstDownload
Publicity Resources
Related Articles
Related Author
Related Institution
- Postal code：510275
- Tel：020-84112585，84113223 Email：xuebaozr@mail.sysu.edu.cn
- Technical support is provided by Beijing Founder electronics co., LTD 京ICP备09064830号-19
京公网安备11010802024621 - It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
- Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.
