On some classes of demicompact linear relation and some results of essential pseudospectra |
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| Author |
ammar aymen84@yahoo.fr1, Aref.Jeribi@fss.rnu.tn2, saadaoui.bilel@hotmail.fr3
Departement of Mathematics,
University of Sfax,
Faculty of Sciences of Sfax,
Tunisia
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| Abstract |
The main goal of this paper is to give some perturbation results and some relations between
the essential pseudospectra of the sum of two multivalued linear operator and the essential
pseudospectra of each of these multivalued linear operator.
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| Keywords |
demicompact; pseudospectra; linear relation
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| DOI |
doi:10.30970/ms.52.2.195-210
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| Reference |
1. A. Jeribi, Spectral theory and applications of linear operator and block operator matrices, Springer-
Verlag, New York, 2015.
2. F. Abdmouleh, A. Jeribi, T. Alvarez, On a characterization of the essential spectra of a linear relation, 2012, preprint. 3. T. Alvarez, A. Ammar, A. Jeribi, A characterization of some subsets of S-essential spectra of a multivalued linear operator, Colloq. Math., 135 (2014), 171-186. 4. T. Alvarez, R.W. Cross, D. Wilcox, Multivalued Fredholm type operators with abstract generalised inverses, J. Math. Anal. Appl., 261 (2001), №1, 403-417. 5. T. Alvarez, A. Ammar, A. Jeribi, On the essential spectra of some matrix of lineair relations, Math. Methods Appl. Sci., 37 (2014) 620-644. 6. A. Ammar, A. Jeribi, B. Saadaoui, Frobenius-Schur factorization for multivalued 2 Ѓ~ 2 matrices linear operator, Mediterr. J. Math., 14 (2017), №1, 14-29. 7. A. Ammar, A. Jeribi, B. Saadaoui, A characterization of essential pseudospectra of the multivalued operator matrix, Anal. Math. Phys., DOI 10.1007/s13324-017-0170-z. 8. A. Ammar, A. Jeribi, B. Saadaoui, Demicompactness, Slection of linear relation and application to multivalued matrix, Preprint, 2018. 9. A. Ammar, H. Daoud, A. Jeribi, Pseudospectra and essential pseudospectra of multivalued linear relations, Mediterr. J. Math. 12 (2015), no. 4, 1377-1395. 10. A. Ammar, H. Daoud, A. Jeribi, The stability of pseudospectra and essential pseudospectra of linear relation, J. Pseudo-Differ. Oper. Appl., 7 (2016), №4, 473-491. 11. W.Chaker, A. Jeribi, B. Krichen, Demicompact linear operators, essential spectrum and some perturbation results, Math. Nachr., 288 (2015), №13, 1476-1486. 12. E. Chafai, M. Mnif, Perturbation of normally solvable linear relations in paracomplete spaces, Linear Algebra Appl., 439 (2013), №7, 1875-1885. 13. R.W. Cross, Multivalued linear operators, Marcel Dekker, 1998. 14. R.W. Cross, An index theorem for the product of linear relations, Linear Algebra Appl., 277 (1998), 127-134. 15. E.B. Davies, Linear Operators and their spectra, Cambridge Studies in Advanced Mathematics, 106, Camb. Univ. Press, Cambridge, 2007. 16. B. Krichen, Relative essential spectra involving relative demicompact unbounded linear operators, Acta Math. Sci. Ser. B Engl. Ed., 34 (2014), №2, 546–556. 17. H.J. Landau, On Szego’s eigenvalue distribution theorem and non-Hermitian kernels, J. Anal. Math., 28 (1975), 335–357. 18. W.V. Petryshyn, Construction of fixed points of demicompact mappings in Hilbert space, J. Math. Anal. Appl., 14 (1966), 276–284. 19. L.N. Trefethen, Pseudospectra of matrices, numerical analysis, 1991, In Pitman Research notes in Mathematics Series, Longman Science and Technology, Harlow 260, 1992, 234–266. 20. L.N. Trefethen, Pseudospectra of linear operators, SAIM rev., 39 (1997), 383–406. 21. J.M. Varah, The computation of bounds for the invariant subspaces of a general matrix operator, Ph.D. thesis, stanford university ProQuest LLC, Ann Arbor, 1967. 22. J.H. Wilkinson, Sensitivity of eigenvalues II, Util. Math., 30 (1986), 243–286. |
| Pages |
195-210
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| Volume |
52
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| Issue |
2
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| Year |
2019
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| Journal |
Matematychni Studii
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| Full text of paper | |
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