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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Main Author: J. Ettayb
Format: Article
Language:English
Published: Academician Ye.A. Buketov Karaganda University 2024-12-01
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
description 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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publisher Academician Ye.A. Buketov Karaganda University
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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