Geodesic
A characterization of s-pseudospectra of linear operators in a Hilbert space
Filomat, Tome 37 (2023) no. 5, p. 1331

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DOI

In this work, we introduce and study the S-pseudospectra of linear operators defined by non-strict inequality in a Hilbert space. Inspired by A. Böttcher'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 ε.
DOI : 10.2298/FIL2305331A
Classification : 47A53, 47A55, 47A10
Keywords: S-pseudospectra, S-spectrum, linear operator, Hilbert space 
Aymen Ammar; Ameni Bouchekoua; Aref Jeribi. A characterization of s-pseudospectra of linear operators in a Hilbert space. Filomat, Tome 37 (2023) no. 5, p. 1331 . doi: 10.2298/FIL2305331A
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     title = {A characterization of s-pseudospectra of linear operators in a {Hilbert} space},
     journal = {Filomat},
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     year = {2023},
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     doi = {10.2298/FIL2305331A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2305331A/}
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