On isolated points of the approximate point spectrum of a closed linear relation

• Melik Lajnef ^[1] ; Maher Mnif ^[1]
  1. [1] University of Sfax

     University of Sfax

     Túnez

     
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 37, Nº 1, 2022, págs. 75-90
• Idioma: inglés
• DOI: 10.17398/2605-5686.37.1.75
• Enlaces
  • Texto completo
• Resumen

  • We investigate in this paper the isolated points of the approximate point spectrum of a closed linear relation acting on a complex Banach space by using the concepts of quasinilpotent part and the analytic core of a linear relation.

• Referencias bibliográficas
  • [1] T. Álvarez, On regular linear relations, Acta Math. Sin. (Engl. Ser.) 28(2) (2012) 183-194.
  • [2] T. Álvarez, M. Benharrat, Relationship between the Kato spectrum and the Goldberg spectrum of a linear relation. Mediterr. J. Math. 13...
  • [3] T. Álvarez, A. Sandovici, Regular linear relations on Banach spaces. Banach J. Math. Anal. 15 (2021), no. 1, Paper No. 4, 26.
  • [4] Y. Chamkha, M. Kammoun, On perturbation of Drazin invertible linear relations, to appear in Ukrainian Mathematical Journal (2021).
  • [5] R. W. Cross, Multivalued linear operators, Pure and Applied Mathematics, Marcel Dekker, (1998).
  • [6] A. Favini, A. Yagi, Multivalued linear operators and degenerate evolution equations, Annali di Mat. Pura Appl. 163, 353-384 (1993).
  • [7] A. Ghorbel, M. Mnif, Drazin inverse of multivalued operators and its applications, Monatsh Math (2019) 273-293.
  • [8] M. González, M. Mbekhta, M. Oudghiri, On the isolated points of the surjective spectrum of a bounded operator. Proc. Amer. Math. Soc....
  • [9] M. Lajnef, M. Mnif, Isolated spectral points of a linear relation. Monatsh. Math. 191 (2020), pp. 595-614.
  • [10] M. Lajnef, M. Mnif, On generalized Drazin invertible linear relations. Rocky Mountain J. Math. 50 (2020), no. 4, 1387-1408.
  • [11] M. Mbekhta, Généralisation de la décomposition de Kato aux opérateurs paranormaux et spectraux, Glasgow Math. J. 29 (1987), pp. 159-175.
  • [12] M. Mnif and A.A. Ouled-Hmed, Analytic core and quasi-nilpotent part of linear relations in Banach spaces, Filomat 32 (2018), no 7, 2499-2515.