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Ufa Mathematical Journal, 2024, Volume 16, Issue 3, Pages 125–133
DOI: https://doi.org/10.13108/2024-16-3-125 (Mi ufa705) 		 
On level sets of norm of generalized resolvent of operators pencils

M. A. Mansouria, A. Khellafab, H. Guebbaia

a Laboratoire des Mathématiques Appliquées et Modélisation, Department of Mathematics, Université 8 Mai 1945, BP.401, Guelma, 24000, Algeria
b Ecole Nationale Polytechniques de Constantine, Nouvelle Ville of Ali Mendjeli, BP 75, 25000, Constantine, Algeria
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DOI: https://doi.org/10.13108/2024-16-3-125
Abstract: We prove that the generalized resolvent operator defined in a Hilbert space cannot remain constant on any open subset of the resolvent set. Under certain conditions we also prove the same result for a complex uniformly convex Banach space. These results extend the known ones.
Keywords: $\varepsilon$–pseudospectrum, $\varepsilon$–pseudospectrum of operators pencils, generalized spectrum approximation, operator pencil.
Received: 22.12.2023
Document Type: Article
MSC: 35P15, 47A75, 35J10
Language: English
Original paper language: English
Citation: M. A. Mansouri, A. Khellaf, H. Guebbai, “On level sets of norm of generalized resolvent of operators pencils”, Ufa Math. J., 16:3 (2024), 125–133
Citation in format AMSBIB
\Bibitem{ManKheGue24}
\by M.~A.~Mansouri, A.~Khellaf, H.~Guebbai
\paper On level sets of norm of generalized resolvent of operators pencils
\jour Ufa Math. J.
\yr 2024
\vol 16
\issue 3
\pages 125--133
\mathnet{http://mi.mathnet.ru/eng/ufa705}
\crossref{https://doi.org/10.13108/2024-16-3-125}
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