Affiliation:
1. Department of Mathematics, University of Sfax, Faculty of Sciences of Sfax, Sfax, Tunisia
Abstract
In this work, we introduce and study the S-pseudospectra of linear operators defined by nonstrict inequality in a Hilbert space. Inspired by A. B?ttcher?s result [3], we prove that the S-resolvent norm of bounded linear operators is not constant in any open set of the S-resolvent set. Beside, we find a characterization of the S-pseudospectrum of bounded linear operator by means the S-spectra of all perturbed operators with perturbations that have norms strictly less than ?.
Publisher
National Library of Serbia
Reference12 articles.
1. A. Ammar and A. Jeribi, A characterization of the essential pseudospectra and application to a transport equation, Extracta Math. 28, no. 1, 95-112, (2013).
2. A. Ammar and A. Jeribi, The essential pseudo-spectra of a sequence of linear operators, Complex Anal. Oper. Theory 12, no. 3, 835-848, (2018).
3. A. Böttcher, Pseudospectra and singular values of large convolution operators, J. Integral Equations Appl. 6 , no. 3, 267-301, (1994).
4. V. Fraysse, M. Gueury, F. Nicoud and V. Toumazou, Spectral portraits for matrix pencils (1996).
5. A. Jeribi, Spectral theory and applications of linear operators and block operator matrices, Springer-Verlag, New York, (2015).