Generalized Drazin-type spectra of Operator matrices.
Keywords:
Surjective spectrum, Approximate point spectrum, Generalized Drazin spectrum, Single-valued extension property, Operator matricesAbstract
In this paper, we investigate the limit points set of surjective and approximate point spectra of upper triangular operator matrices . We prove that σ*(MC) ∪ W=σ*(A)∪ σ*(B) where W is the union of certain holes in σ*(MC), which happen to be subsets of σlgD(B) ∩ σrgD(A), σ* ∈ {σlgD, σrgD} are the limit points set of surjective and approximate point spectra. Furthermore, several sufficient conditions for σ* (MC) = σ* (A)∪σ* (B) holds for every C ∈ ℬ(Y,X) are given.
References
P. Aiena. Fredholm and Local Spectral Theory with Applications to Multipliers. Kluwer. Acad. Press, (2004).
C. Benhida, E. H. Zerouali, H. Zguitti. Spectra of upper triangular operator matrices, Proc. Am. Math. Soc. Vol 133, Num 10, pp. 3013-3020, (2005).
M. Houmidi, H. Zguitti, Propriétés spectrales locales d’une matrice carrée des opérateurs, Acta Math. Vietnam. 25, pp. 137-144, (2000).
K. B.Laursen, M. M. Neumann. An introduction to Local Spectral Theory in: London Mathematical Society Monograph, New series, Vol. 20, Clarendon Press, Oxford, (2000).
J. J. Koliha. A generalized Drazin inverse. Glasgow Math. J., 38 : pp. 367-81, (1996).
H. Zariouh, H. Zguitti. On pseudo B-Weyl operators and generalized drazin invertible for operator matrices, Linear and Multilinear Algebra, Vol 64, Issue 7, pp. 1245-1257, (2016).
E. H. Zerouali, H. Zguitti. Perturbation of spectra of operator matrices and local spectral theory, J. Math Anal Appl, 324: pp. 992-1005, (2006).
S. Zhang, H.Zhong, L. Lin. Generalized Drazin Spectrum of Operator Matrices, Appl. Math. J. Chinese Univ. 29 (2), pp. 162-170, (2014).
S. F. Zhang, H. J. Zhang, J. D. Wu. Spectra of upper-triangular operator matrices, Acta Math Sinica (in Chinese), 2011, 54: 41-60, (2011).
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.