Home S-essential spectra and measure of noncompactness
Article
Licensed
Unlicensed Requires Authentication

S-essential spectra and measure of noncompactness

  • Chafika Belabbaci EMAIL logo , Mouloud Aissani and Mekki Terbeche
Published/Copyright: September 22, 2017
Become an author with De Gruyter Brill

Abstract

In the present paper we give some results concerning the S-essential spectra of linear bounded operators on a Banach space using the notion of a measure of noncompactness.


(Communicated by Werner Timmermann)


References

[1] Abdelmoumen, B.—Baklouti, H.: Perturbation results on semi-fredholm operators and applications, J. Inequal. Appl. 2009, Art. ID 284526, 13 pp.10.1155/2009/284526Search in Google Scholar

[2] Abdmouleh, F.—Ammar, A.—Jeribi, A.: Stability of the s-essential spectra on a Banach space, Math. Slovaca 63 (2013), 299–320.10.2478/s12175-012-0099-5Search in Google Scholar

[3] Abramovich, Y.—Aliprantis, C. D.: Invitation to Operator Theory. Grad. Stud. Math. 50, Amer. Math. Soc., Providence, 2002.10.1090/gsm/050Search in Google Scholar

[4] Akhmerov, R.—Kamenski, M.—Potapov, A.—Rodkina, A.—Sadovskii, B.: Measures of Noncompactness and Condensing Operators. Oper. Theory Adv. Appl. 55, Birkhäuser Verlag, Basel, Boston, Berlin, 1992.10.1007/978-3-0348-5727-7Search in Google Scholar

[5] Ammar, A.—Boukettaya, B.—Jeribi, A.: Stability of the s-left and s-right essential spectra of a linear operator, Acta Math. Sci. 34 (2014), 1922–1934.10.1016/S0252-9602(14)60135-1Search in Google Scholar

[6] Ammar, A.— Zerai Dhahri, M.—Jeribi, A.: A characterization of s-essential spectrum by means of measure of non-strict-singularity and application, Azerb. J. Math. 1 (2015).Search in Google Scholar

[7] Banas, J.—Mursaleen, M.: Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations, Springer, 2014.10.1007/978-81-322-1886-9Search in Google Scholar

[8] Edmunds, D.—Evans, W. D.: Spectral Theory and Differential Operators. Oxford Mathematical Monographs, Clarendon Press, 1987.Search in Google Scholar

[9] Furi, M.—Martelli, M.—Vignoli, A.: Contributions to the spectral theory for nonlinear operators in banach spaces, Ann. Mat. Pura Appl. 118 (1978), 229–294.10.1007/BF02415132Search in Google Scholar

[10] Goldberg, S.: Unbounded Linear Operators, McGraw-Hill, New York, 1966.Search in Google Scholar

[11] Jeribi, A.: Spectral Theory and Applications of Linear Operators and Block Operator Matrices, Springer, New York, 2015.10.1007/978-3-319-17566-9Search in Google Scholar

[12] Jeribi, A.—Moalla, N.—Yengui, S.: S-essential spectra and application to an example of transport operators, Math. Methods Appl. Sci 37 (2014), 2341–2353.10.1002/mma.1564Search in Google Scholar

[13] Kato, T.: Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Anal. Math. 6 (1958), 261–322.10.1007/BF02790238Search in Google Scholar

[14] Kato, T.: Perturbation Theory for Linear Operators. Die Grundlehren der mathematischen Wissenschaften 132, Springer-Verlag, Berlin, Heidelberg, New York, 1966.Search in Google Scholar

[15] Malkowsky, E.—Rakočević, V.: An introduction into the theory of sequence spaces and measures of noncompactness, Zbornik radova, Matematicki institut SANU 9 (2000), 143–234.Search in Google Scholar

[16] Markus, A.: Introduction to the Spectral Theory of Polynomial Operator Pencils. Transl. Math. Monogr. 71, Amer. Math. Soc., 1988.Search in Google Scholar

[17] Müller, V.: Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras. Oper. Theory Adv. Appl. 139, 2nd edition, Birkhäuser, Basel, Boston, Berlin, 2007.Search in Google Scholar

[18] Schechter, M.: Principles of Functional Analysis. Grad. Stud. Math. 36, 2nd edition, Amer. Math. Soc., Providence, Rhode Island, 2002.Search in Google Scholar

[19] Toledano, J.—Benavides, T.—Acedo, G.: Measures of Noncompactness in Metric Fixed Point Theory. Oper. Theory Adv. Appl. 99, Springer Basel AG, 1997.10.1007/978-3-0348-8920-9Search in Google Scholar

Received: 2015-9-6
Accepted: 2016-2-2
Published Online: 2017-9-22
Published in Print: 2017-10-26

© 2017 Mathematical Institute Slovak Academy of Sciences

Downloaded on 25.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ms-2017-0043/html
Scroll to top button