Research ArticleOpen AccessGoogle Scholar indexed
Spectra of 2 × 2 Upper-Triangular Operator Matrices
College of Mathematics and Information Science, Shangqiu Normal University, Shangqiu, China
- 1 College of Mathematics and Information Science, Shangqiu Normal University, Shangqiu, China
Applied Mathematics·Volume 04 (2013)·Pages 22–25·Published 16 October 2013·DOI10.4236/am.2013.411A1004
Copy link · social · email
Abstract
In [Perturbation of Spectrums of 2 × 2 Operator Matrices, Proceedings of the American Mathematical Society , Vol. 121, 1994], the authors asked whether there was an operator such that for a given pair ( A , B ) of operators, where the operator was defined by . In this note, a partial answer for the question is given.
KeywordsSpectraUpper-Triangular Operator MatrixFredholm Operator
- H. K. Du and J. Pan, “Perturbation of Spectrums of 2 × 2 Operator Matrices,” Proceedings of the American Mathematical Society, Vol. 121, 1994, pp. 761-766. http://dx.doi.org/10.1090/S0002-9939-1994-1185266-2
- H. Y. Zhang and H. K. Du, “Browder Spectra of Upper Triangular Operator Matrices,” Journal of Mathematical Analysis and Applications, Vol. 323, No. 1, 2006, pp. 700-707. http://dx.doi.org/10.1016/j.jmaa.2005.10.073
- M. Barrua and M. Boumazgour, “A Note on the Spectra of an Upper Triangular Operator Matrix,” Proceedings of the American Mathematical Society, Vol. 131, 2003, pp. 3083-3088. http://dx.doi.org/10.1090/S0002-9939-03-06862-X
- X. H. Cao and B. Meng, “Essential Appoximate Point Spectra and Weyl’s Theorem for Operator Matices,” Journal of Mathematical Analysis and Applications, Vol. 304, No. 2, 2005, pp. 759-771. http://dx.doi.org/10.1016/j.jmaa.2004.09.053
- D. S. Djordjevic, “Perturbations Spectra of Operator Matrices,” Journal of Operator Theory, Vol. 48, 2002, pp. 467-486.
- J. K. Han, H. Y. Lee and W. Y. Lee, “Invertible Completions of 2 × 2 Operator Matrices,” Proceedings of the American Mathematical Society, Vol. 128, 2000, pp. 119123. http://dx.doi.org/10.1090/S0002-9939-99-04965-5
- Y. Li, X. H. Sun and H. K. Du, “Inversctions of the Left and Right Essential Spectra of 2 × 2 Upper Triangular Operator Matrices,” Bulletin London Mathematical Society, Vol. 36, 2004, pp. 811-819.
- H. Y. Zhang, X. H. Zhang and H. K. Du, “Drazin Spectra of 2 × 2 Upper Triangular Operator Matrices,” Acta Mathematica Scientia, Vol. 29, 2009, pp. 272-282.
- J. B. Conwey, “A Course in Functional Analysis,” Springer-verlag, New York, Heidelberg, Berlin, Tokyo, 1985. http://dx.doi.org/10.1007/978-1-4757-3828-5