Pseudospectra of the direct sum of linear operators in ultrametric Banach spaces
In this paper, a characterization of essential pseudospectra of bounded linear operators on ultrametric Banach spaces over a spherically complete field was given and the notions of pseudospectra and condition pseudospectra of the direct sum of linear operators on ultrametric Banach spaces were intr...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2024-12-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
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| Online Access: | https://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/886 |
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| author | J. Ettayb |
| author_facet | J. Ettayb |
| author_sort | J. Ettayb |
| collection | DOAJ |
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In this paper, a characterization of essential pseudospectra of bounded linear operators on ultrametric Banach spaces over a spherically complete field was given and the notions of pseudospectra and condition pseudospectra of the direct sum of linear operators on ultrametric Banach spaces were introduced. In particular, we proved that the pseudospectra of the direct sum of bounded linear operators associated with various ε are nested sets and that the intersection of all the pseudospectra of bounded linear operators is the spectrum of the direct sum of bounded linear operators in the direct sum of ultrametric Banach spaces. In addition, many results were proved about them and examples were given.
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| format | Article |
| id | doaj-art-fdf87583d7414f0389aa01564a7f5bf0 |
| institution | Kabale University |
| issn | 2518-7929 2663-5011 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj-art-fdf87583d7414f0389aa01564a7f5bf02024-12-30T08:04:44ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112024-12-01116410.31489/2024m4/107-118Pseudospectra of the direct sum of linear operators in ultrametric Banach spacesJ. Ettayb 0https://orcid.org/0000-0002-4819-943XRegional Academy of Education and Training of Casablanca-Settat, Hamman Al-Fatawaki Collegiate High School, Had Soualem, Berrechid Province, Morocco In this paper, a characterization of essential pseudospectra of bounded linear operators on ultrametric Banach spaces over a spherically complete field was given and the notions of pseudospectra and condition pseudospectra of the direct sum of linear operators on ultrametric Banach spaces were introduced. In particular, we proved that the pseudospectra of the direct sum of bounded linear operators associated with various ε are nested sets and that the intersection of all the pseudospectra of bounded linear operators is the spectrum of the direct sum of bounded linear operators in the direct sum of ultrametric Banach spaces. In addition, many results were proved about them and examples were given. https://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/886Ultrametric Banach spacespseudospectrumcondition pseudospectrumdirect sum of operatorslinear operator pencils |
| spellingShingle | J. Ettayb Pseudospectra of the direct sum of linear operators in ultrametric Banach spaces Қарағанды университетінің хабаршысы. Математика сериясы Ultrametric Banach spaces pseudospectrum condition pseudospectrum direct sum of operators linear operator pencils |
| title | Pseudospectra of the direct sum of linear operators in ultrametric Banach spaces |
| title_full | Pseudospectra of the direct sum of linear operators in ultrametric Banach spaces |
| title_fullStr | Pseudospectra of the direct sum of linear operators in ultrametric Banach spaces |
| title_full_unstemmed | Pseudospectra of the direct sum of linear operators in ultrametric Banach spaces |
| title_short | Pseudospectra of the direct sum of linear operators in ultrametric Banach spaces |
| title_sort | pseudospectra of the direct sum of linear operators in ultrametric banach spaces |
| topic | Ultrametric Banach spaces pseudospectrum condition pseudospectrum direct sum of operators linear operator pencils |
| url | https://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/886 |
| work_keys_str_mv | AT jettayb pseudospectraofthedirectsumoflinearoperatorsinultrametricbanachspaces |