Upper triangular operator matrices and limit points of the essential spectrum
DOI:
https://doi.org/10.22199/issn.0717-6279-2019-03-0026Keywords:
Fredholm operator, Essential spectra, Limit point, Operator matricesAbstract
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.References
P. Aiena, Semi-Fredholm operators, Perturbation theory and localized SVEP. Caracas: Ediciones IVIC, 2007.
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.
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/2OM2xQS
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.
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.
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.
K. Laursen and M. Neumann, An introduction to local spectral theory. (London Mathematical Society Monograph, New series, vol. 20). Oxford: Clarendon Press, 2000.
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.
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.
Published
How to Cite
Issue
Section
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.