M. A. Mansouri, A. Khellaf, H. Guebbai, “On level sets of norm of generalized resolvent of operators pencils”, Ufimsk. Mat. Zh., 2024, Volume 16, Issue 3,Pages <nobr>130

On level sets of norm of generalized resolvent of operators pencils

M. A. Mansouri^a, A. Khellaf^ab, H. Guebbai^a

^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

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.

MSC: 35P15, 47A75, 35J10

Received: 22.12.2023

Language: English