Generalized trace pseudo-spectrum of matrix pencils
- Aymen Ammar ammar_aymen84@yahoo.fr
- Aref Jeribi aref.Jeribi@fss.rnu.tn
- Kamel Mahfoudhi kamelmahfoudhi72@yahoo.com
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DOI:
https://doi.org/10.4067/S0719-06462019000200065Abstract
The objective of the study was to investigate a new notion of generalized trace pseudo- spectrum for an matrix pencils. In particular, we prove many new interesting properties of the generalized trace pseudo-spectrum. In addition, we show an analogue of the spectral mapping theorem for the generalized trace pseudo-spectrum in the matrix algebra.
Keywords
[1] A. Ammar, A. Jeribi and K. Mahfoudhi, A characterization of the essential approximation pseudo-spectrum on a Banach space, Filomath 31, (11), 3599-3610 (2017).
[2] A. Ammar, A. Jeribi and K. Mahfoudhi, A characterization of the condition pseudo-spectrum on Banach space, Funct. Anal. Approx. Comput. 10 (2) (2018), 13–21.
[3] Ammar, A., Jeribi, A., Mahfoudhi, K., The essential condition pseudo-spectrum and related results, J. Pseudo-Differ. Oper. Appl., (2018) 1-14.
[4] Ammar, A., Jeribi, A., Mahfoudhi, K., The essential approximate pseudo-spectrum and related results, Filomat, 32, 6, (2018), 2139-2151.
[5] Ammar, A., Jeribi, A.,Mahfoudhi, K., A characterization of Browder‘s essential approximation and his essential defect pseudo-spectrum on a Banach space, Extracta Math. ,34 (1) (2019), 29-40.
[6] A. Jeribi. Spectral theory and applications of linear operators and block operator matrices, Springer-Verlag, New-York, (2015).
[7] R.A. Horn, C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, (1991).
[8] Krishna Kumar. G, Determinant spectrum: A generalization of eigenvalues, Funct. Anal. Approx. Comput. 10 (2) (2018), 1–12.
[9] L. N. Trefethen and M. Embree, Spectra and pseudo-spectra: The behavior of non normal matrices and operators. Prin. Univ. Press, Princeton and Oxford, (2005).
[2] A. Ammar, A. Jeribi and K. Mahfoudhi, A characterization of the condition pseudo-spectrum on Banach space, Funct. Anal. Approx. Comput. 10 (2) (2018), 13–21.
[3] Ammar, A., Jeribi, A., Mahfoudhi, K., The essential condition pseudo-spectrum and related results, J. Pseudo-Differ. Oper. Appl., (2018) 1-14.
[4] Ammar, A., Jeribi, A., Mahfoudhi, K., The essential approximate pseudo-spectrum and related results, Filomat, 32, 6, (2018), 2139-2151.
[5] Ammar, A., Jeribi, A.,Mahfoudhi, K., A characterization of Browder‘s essential approximation and his essential defect pseudo-spectrum on a Banach space, Extracta Math. ,34 (1) (2019), 29-40.
[6] A. Jeribi. Spectral theory and applications of linear operators and block operator matrices, Springer-Verlag, New-York, (2015).
[7] R.A. Horn, C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, (1991).
[8] Krishna Kumar. G, Determinant spectrum: A generalization of eigenvalues, Funct. Anal. Approx. Comput. 10 (2) (2018), 1–12.
[9] L. N. Trefethen and M. Embree, Spectra and pseudo-spectra: The behavior of non normal matrices and operators. Prin. Univ. Press, Princeton and Oxford, (2005).
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Published
2019-08-10
How to Cite
[1]
A. . Ammar, A. Jeribi, and K. Mahfoudhi, “Generalized trace pseudo-spectrum of matrix pencils”, CUBO, vol. 21, no. 2, pp. 65–76, Aug. 2019.
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