On isolated points of the approximate point spectrum of a closed linear relation
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Abstract
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.
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How to Cite
Lajnef, M., & Mnif, M. (2022). On isolated points of the approximate point spectrum of a closed linear relation. Extracta Mathematicae, 37(1), 75-90. https://doi.org/10.17398/2605-5686.37.1.75
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Section
Operator Theory
References
[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 (2016), no. 1, 365-378.
[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. 136 (2008), no. 10, 3521-3528.
[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.
[2] T. Álvarez, M. Benharrat, Relationship between the Kato spectrum and the Goldberg spectrum of a linear relation. Mediterr. J. Math. 13 (2016), no. 1, 365-378.
[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. 136 (2008), no. 10, 3521-3528.
[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.