On level sets of norm of generalized resolvent of operators pencils

Authors

  • M.A. Mansouri
    Laboratoire des Mathematiques Appliquees et Modelisation, Department of Mathematics Universite 8 Mai 1945, Algeria
  • A. Khellaf
    École Nationale Polytechnique de Constantine, Algeria
    Laboratoire des Mathematiques Appliquees et Modelisation, Department of Mathematics Universite 8 Mai 1945, Algeria
  • H. Guebbai
    Laboratoire des Mathematiques Appliquees et Modelisation, Department of Mathematics Universite 8 Mai 1945, Algeria

DOI:

https://doi.org/10.13108/2024-16-3-125

Keywords:

$\varepsilon$--pseudospectrum, $\varepsilon$--pseudospectrum of operators pencils, generalized spectrum approximation, operator pencil

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.

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Published

12.09.2024

Issue

Vol. 16 No. 3 (2024): Ufa Mathematical Journal 2024, volume 16, issue 3

Section

Article