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Matematicheskie Zametki, 2024, Volume 115, Issue 6, paper published in the English version journal (Mi mzm14234)  
Papers published in the English version of the journal

On the Convergence of Generalized Pseudo-Spectrum

M. A. Mansouriab, A. Khellafbc , H. Guebbaiab

a Département de Mathématiques, Université 8 mai 1945, Guelma, Algérie
b Laboratoire de Mathématiques Appliquées et Modélisation (LMAM), Université 8 mai 1945, Guelma, Algérie
c École Nationale Polytechnique de Constantine, Constantine, Algérie
Abstract: In this paper, we study the convergence of generalized pseudo-spectrum associated with bounded operators in a Hilbert space. We prove that the approximate generalized pseudo-spectrum converges to the exact set under norm convergence. To prove this result, we use the Hausdorff distance and the assumption that the generalized resolvent operator is not constant on any open subset of the generalized resolvent set.
Keywords: generalized pseudo-spectrum, approximated generalized pseudo-spectrum, Hausdorff distance.
Received: 25.01.2024
Revised: 18.03.2024
English version:
Mathematical Notes, 2024, Volume 115, Issue 6, Pages 973–982
DOI: https://doi.org/10.1134/S0001434624050316
Bibliographic databases:
Document Type: Article
MSC: 34L16, 47A75, 35J10
Language: English
Citation: M. A. Mansouri, A. Khellaf, H. Guebbai, “On the Convergence of Generalized Pseudo-Spectrum”, Math. Notes, 115:6 (2024), 973–982
Citation in format AMSBIB
\Bibitem{ManKheGue24}
\by M.~A.~Mansouri, A.~Khellaf, H.~Guebbai
\paper On the Convergence of Generalized Pseudo-Spectrum
\jour Math. Notes
\yr 2024
\vol 115
\issue 6
\pages 973--982
\mathnet{http://mi.mathnet.ru/mzm14234}
\crossref{https://doi.org/10.1134/S0001434624050316}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4781281}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85198649666}
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