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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.3 Antofagasta ago. 2019

http://dx.doi.org/10.22199/issn.0717-6279-2019-03-0026 

Articles

Upper triangular operator matrices and limit points of the essential spectrum

M. Karmouni1 

A. Tajmouati2 

A. El Bakkali3 

1Cadi Ayyad University, Multidisciplinary Faculty, Sidi Bouzid, B.P. 4162, 46000 Safí, Morocco. e-mail : mohammed.karmouni@uca.ma

2Sidi Mohamed Ben Abdellah University, Faculty of Sciences Dhar Al Mahraz, Laboratory of Mathematical Analysis and Applications, Fez, Morocco. e-mail: abdelaziz.tajmouati@usmba.ac.ma

3Chouaib Doukkali University, Faculty of Science, Department of Mathematics, 24000, Eljadida, Morocco. email : abdeslamelbakkalii@gmail.com

Abstract

In this paper, we investigate the limit points set of essential spectrum of upper triangular operator matrices

We prove that accσe(MC) ∪ W = accσe(A) ∪ accσe(B) where W is the union of certain holes in accσe(MC), which happen to be subsets of accσe(B) ∩ accσe(A). Also, several sufficient conditions for accσe(MC) = accσe(A) ∪ accσe(B) holds are given.

Keywords : Fredholm operator; Essential spectra; Limit point; Operator matrices.

Mathematics Subject Classification (2000):  47A10; 47A11

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

Acknowledgement

The authors thank the referees for his suggestions and comments thorough reading of the manuscript.

References:

[1] P. Aiena, Semi-Fredholm operators, Perturbation theory and localized SVEP. Caracas: Ediciones IVIC, 2007. [ Links ]

[2] C. Benhida, E. Zerouali and H. Zguitti, “Spectra of upper triangular operator matrices”, Proceedings of the American Mathematical Society, vol. 133, no. 10, pp. 3013-3021, 2005, doi: 10.1090/s0002-9939-05-07812-3. [ Links ]

[3] D. Djordjevic, “Perturbations of spectra of operator matrices”, Journal of Operator Theory, vol. 48, no. 3, pp. 467-486, 2002. [On line]. Available: http://bit.ly/2OM2xQSLinks ]

[4] S. Djordević and Y. Han, “A note on Weyl's theorem for operator matrices”, Proceedings of the American Mathematical Society , vol. 131, no. 8, pp. 2543-2548, doi: 10.1090/s0002-9939-02-06808-9. [ Links ]

[5] H. Du and P. Jin, “Perturbation of spectrum of 2×2 operator matrices”, Proceedings of the American Mathematical Society , vol. 121, no. 3, pp.761-766, doi: 10.1090/S0002-9939-1994-1185266-2. [ Links ]

[6] J. Han, H. Lee and W. Lee, “Invertible completions of 2×2 upper triangular operator matrices”, Proceedings of the American Mathematical Society , vol. 128, no. 01, pp. 119-124, 2000, doi: 10.1090/s0002-9939-99-04965-5. [ Links ]

[7] K. Laursen and M. Neumann, An introduction to local spectral theory. (London Mathematical Society Monograph, New series, vol. 20). Oxford: Clarendon Press, 2000. vol. 20. [ Links ]

[8] E. Zerouali and H. Zguitti, “Perturbation of spectra of operator matrices and local spectral theory,” Journal of Mathematical Analysis and Applications, vol. 324, no. 2, pp. 992-1005, 2006, doi: 10.1016/j.jmaa.2005.12.065. [ Links ]

[9] Y. Zhang, H. Zhong, and L. Lin, “Browder spectra and essential spectra of operator matrices,”Acta Mathematica Sinica, English Series, vol. 24, no. 6, pp. 947-954, 2008,doi: 10.1007/s10114-007-6339-x. [ Links ]

Received: November 2017; Accepted: May 2019

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