Stability of some essential B-spectra of pencil operators and application

• Ben Ali, A. ^[1] ; M. Boudhief ^[1] ; N. Moalla ^[1]
  1. [1] University of Sfax

     University of Sfax

     Túnez

     
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 36, Nº 1, 2021, págs. 63-80
• Idioma: inglés
• DOI: 10.17398/2605-5686.36.1.63
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• Resumen

  • In this paper, we give some results on the essential B-spectra of a linear operator pencil, which are used to determine the essential B-spectra of an integro-differential operator with abstract boundary conditions in the Banach space Lp([−a, a] × [−1, 1]), p ≥ 1 and a > 0.

• Referencias bibliográficas
  • [1] P. Aiena, “ Fredholm and Local Spectral Theory II, with Applications to Weyl-type theorems ”, Lecture Notes in Mathematics, 2235, Springer,...
  • [2] M. Berkani, On a class of quasi-Fredholm operators, Integral Equations Operator Theory 34 (1999), 244 – 249.
  • [3] M. Berkani, Restriction of an operator to the range of its powers, Studia Math. 140 (2000), 163 – 175.
  • [4] M. Berkani, B-Weyl spectrum and poles of the resolvent, J. Math. Anal. Appl. 272 (2002), 596 – 603.
  • [5] M. Berkani, On the B-Fredholm Alternative, Mediterr. J. Math. 10 (2013), 1487 – 1496.
  • [6] M. Berkani, M. Boudhief, N. Moalla, Stability of essential B-spectra of unbounded linear operators and applications, to appear in Afrika...
  • [7] M. Berkani, M. Boudhief, N. Moalla, A characterization of unbounded generalized meromorphic operators, to appear in Filomat.
  • [8] M. Benharrat, B. Messirdi, Relationship between a variant of essential spectrum and the Kato essential, Gen. Math. 20 (4) (2012), 71 –...
  • [9] M. Benharrat, B. Messirdi, Relationship between the essential quasi-Fredholm spectrum and the closed-range spectrum, An. Univ. Oradea...
  • [10] M. Berkani, N. Moalla, B-Fredholm properties of closed invertible operators, Mediterr. J. Math. 13 (2016), 4175 – 4185.
  • [11] M. Barkani, M. Sarih, On semi B-Fredholm operators, Glasg. Math. J. 43 (2001), 457 – 465.
  • [12] A. Gherbi, B. Messirdi, M. Amouch, A spectral analysis of linear operator pencils on Banach spaces with application to quotient of bounded...
  • [13] A. Jeribi, “ Spectral Theory and Applications of Linear Operators and Block Operator Matrices ”, Springer, Cham, 2015.
  • [14] A. Jeribi, “ Linear Operators and their Essential Pseudospectra ”, Apple Academic Press, Oakville, ON, 2018.
  • [15] A. Jeribi, N. Moalla, S. Yengui, S-essential spectra and application to an example of transport operators, Math. Methods Appl. Sci. 37...
  • [16] Q. Jiang, Q. Zeng, H. Zhong, Spectra originating from semi-B-Fredholm theory and commuting perturbations, Studia Math. 219 (2013), 1...
  • [17] J.P. Labrousse, Les opérateurs quasi-Fredholm: une généralisation des opérateurs semi-Fredholm, Rend. Circ. Mat. Palermo (2) 29 (1980),...
  • [19] M. Schechter, “ Principles of Functional Analysis ”, Academic Press, New York-London, 1971.
  • [20] P. Saphar, Contribution à l’étude des applications linéaires dans un espace de Banach, Bull. Soc. Math. France 92 (1964), 363 – 384.