Upper triangular operator matrices and limit points of the essential spectrum

• Karmouni, Mohammed ^[1] ; Tajmouati, A. ^[2] ; A. El Bakkali, A. ^[3]
  1. [1] Cadi Ayyad University

     Cadi Ayyad University

     Marrakech-Medina, Marruecos

     
  2. [2] Sidi Mohamed Ben Abdellah University

     Sidi Mohamed Ben Abdellah University

     Fes-Medina, Marruecos

     
  3. [3] Université Chouaib Doukkali

     Université Chouaib Doukkali

     Marruecos

     

  Mostrar afiliaciones +
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 38, Nº. 3, 2019, págs. 401-409
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2019-03-0026
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we investigate the limit points set of essential spectrum of upper triangular operator matrices We prove that accσe(MC) ∪ W = accσe(A) ∪ accσe(B) where W is the union of certain holes in accσe(MC), which happen to be subsets of accσe(B) ∩ accσe(A). Also, several sufficient conditions for accσe(MC) = accσe(A) ∪ accσe(B) holds are given.

• Referencias bibliográficas
  • P. Aiena, Semi-Fredholm operators, Perturbation theory and localized SVEP. Caracas: Ediciones IVIC, 2007.
  • C. Benhida, E. Zerouali and H. Zguitti, “Spectra of upper triangular operator matrices”, Proceedings of the American Mathematical Society,...
  • D. Djordjevic, “Perturbations of spectra of operator matrices”, Journal of Operator Theory, vol. 48, no. 3, pp. 467-486, 2002. [On line]....
  • S. Djordević and Y. Han, “A note on Weyl's theorem for operator matrices”, Proceedings of the American Mathematical Society, vol. 131,...
  • H. Du and P. Jin, “Perturbation of spectrum of 2×2 operator matrices”, Proceedings of the American Mathematical Society, vol. 121, no. 3,...
  • J. Han, H. Lee and W. Lee, “Invertible completions of 2×2 upper triangular operator matrices”, Proceedings of the American Mathematical Society,...
  • K. Laursen and M. Neumann, An introduction to local spectral theory. (London Mathematical Society Monograph, New series, vol. 20). Oxford:...
  • E. Zerouali and H. Zguitti, “Perturbation of spectra of operator matrices and local spectral theory”, Journal of Mathematical Analysis and...
  • Y. Zhang, H. Zhong, and L. Lin, “Browder spectra and essential spectra of operator matrices”, Acta Mathematica Sinica, English Series, vol....