Geodesic
On level sets of norm of generalized resolvent of operators pencils
Ufa mathematical journal, Tome 16 (2024) no. 3, pp. 125-133

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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. 
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     title = {On level sets of norm of generalized resolvent of operators pencils},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2024_16_3_a10/}
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M. A. Mansouri; A. Khellaf; H. Guebbai. On level sets of norm of generalized resolvent of operators pencils. Ufa mathematical journal, Tome 16 (2024) no. 3, pp. 125-133. http://geodesic.mathdoc.fr/item/UFA_2024_16_3_a10/