On perturbation of Drazin invertible linear relations
UDC 517.98 We study the stability of regular, finite ascent, and finite descent linear relations defined in Banach spaces under commuting nilpotent operator perturbations.  As an application, we give the invariance theorem of Drazin invertible spectrum under these perturbat...
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| Date: | 2023 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2023
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6761 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512508160245760 |
|---|---|
| author | Chamkha, Y. Kammoun, M. Chamkha, Y. Kammoun, M. |
| author_facet | Chamkha, Y. Kammoun, M. Chamkha, Y. Kammoun, M. |
| author_sort | Chamkha, Y. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-03-06T14:27:00Z |
| description | UDC 517.98
We study the stability of regular, finite ascent, and finite descent linear relations defined in Banach spaces under commuting nilpotent operator perturbations.  As an application, we give the invariance theorem of Drazin invertible spectrum under these perturbations. We also focus on the study of some properties of the left and right Drazin invertible linear relations.  It is proved that, for bounded and closed left (resp., right) Drazin invertible linear relation with nonempty resolvent set, $0$ is an isolated point of the associated approximate point spectrum (resp., surjective spectrum). |
| doi_str_mv | 10.37863/umzh.v75i2.6761 |
| first_indexed | 2026-03-24T03:29:54Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-6761 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:29:54Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-67612023-03-06T14:27:00Z On perturbation of Drazin invertible linear relations On perturbation of Drazin invertible linear relations Chamkha, Y. Kammoun, M. Chamkha, Y. Kammoun, M. Drazin invertible linear relation left and right Drazin invertible linear relation perturbation of linear relations UDC 517.98 We study the stability of regular, finite ascent, and finite descent linear relations defined in Banach spaces under commuting nilpotent operator perturbations.  As an application, we give the invariance theorem of Drazin invertible spectrum under these perturbations. We also focus on the study of some properties of the left and right Drazin invertible linear relations.  It is proved that, for bounded and closed left (resp., right) Drazin invertible linear relation with nonempty resolvent set, $0$ is an isolated point of the associated approximate point spectrum (resp., surjective spectrum). УДК 517.98 Про збурення обернених лінійних співвідношень Дразіна Досліджено стабільність регулярних лінійних співвідношень скінченного підйому та скінченного спуску, що визначені в банахових просторах для комутуючих збурень нільпотентного оператора.  Як застосування наведено теорему про інваріантність оберненого спектра Дразіна при таких збуреннях. Також   вивчаються деякі властивості лівих і правих обернених лінійних співвідношень Дразіна.  Доведено, що для обмеженого та замкненого лівого (відповідно, правого) оберненого лінійного співвідношення Дразіна з непорожньою резольвентною множиною, $0$ є ізольованою точкою відповідного наближеного точкового спектра (відповідно, сюр’єктивного спектра). Institute of Mathematics, NAS of Ukraine 2023-03-02 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/6761 10.37863/umzh.v75i2.6761 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 2 (2023); 269 - 286 Український математичний журнал; Том 75 № 2 (2023); 269 - 286 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/6761/9797 Copyright (c) 2023 Yosra Chamkha |
| spellingShingle | Chamkha, Y. Kammoun, M. Chamkha, Y. Kammoun, M. On perturbation of Drazin invertible linear relations |
| title | On perturbation of Drazin invertible linear relations |
| title_alt | On perturbation of Drazin invertible linear relations |
| title_full | On perturbation of Drazin invertible linear relations |
| title_fullStr | On perturbation of Drazin invertible linear relations |
| title_full_unstemmed | On perturbation of Drazin invertible linear relations |
| title_short | On perturbation of Drazin invertible linear relations |
| title_sort | on perturbation of drazin invertible linear relations |
| topic_facet | Drazin invertible linear relation left and right Drazin invertible linear relation perturbation of linear relations |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/6761 |
| work_keys_str_mv | AT chamkhay onperturbationofdrazininvertiblelinearrelations AT kammounm onperturbationofdrazininvertiblelinearrelations AT chamkhay onperturbationofdrazininvertiblelinearrelations AT kammounm onperturbationofdrazininvertiblelinearrelations |