Linear Operators and Their Essential Pseudospectra

Stability of some essential B-spectra of pencil operators and application

“…The present paper is a generalization of the results obtained by A. Jeribi et al in [15] and some of stability results obtained by M. Berkani et al in [6] for the usual essential B-spectra. It generalizes also the works obtained by A. Jeribi in [13,14] about the invariance of the S-essential spectra under weakly compact or strictly singular perturbations, which are not applied in the B-Fredholm theory. So that, we can use, by adding some hypothesis, the perturbations of the B-Fredholm spectra under finite-rank and power finite-rank commuting operators.…”

Relative $$\varepsilon$$-pseudo weak demicompactness and measures of weak noncompactness

“…The standard definition of pseudospectra begins with a closed linear operator T and defines the set (T) for 𝜀 > 0 by Multiple results on pseudospectra are exhibited in [23] as well as in [6]. Inspired by the notion of Weyl pseudospectra, Ammar and Jeribi defined in [2] the following notion of essential pseudospectra of a densely defined closed linear operator T acting on a Banach space X by Several other essential pseudospectra are also defined an studied in [12]. In this research work, we are basically interested in the following essential pseudospectra One of the main problems consists of studying the invariance of the essential pseudospectrum of T subjected to various kinds of perturbation (see for instance [12] ).…”

“…Inspired by the notion of Weyl pseudospectra, Ammar and Jeribi defined in [2] the following notion of essential pseudospectra of a densely defined closed linear operator T acting on a Banach space X by Several other essential pseudospectra are also defined an studied in [12]. In this research work, we are basically interested in the following essential pseudospectra One of the main problems consists of studying the invariance of the essential pseudospectrum of T subjected to various kinds of perturbation (see for instance [12] ). Recently, in [4], Ben Brahim et al, gave a refinement and investigated the stability of these essential pseudospectra by means of the class of demicompact and pseudo demicompact linear operators.…”

“…The purpose of this study is to pursue the analysis started in [4,12,13] and to extend it to the essential pseudospectra of closed linear operators on a Banach space X. We use this fruitful approach to study the invariance of the essential pseudospectra of these operators, subject to various kinds of perturbation.…”

Essential pseudospectra involving demicompact and pseudodemicompact operators and some perturbation results

“…where B ∈ L(X, Y) and C ∈ L(Z, X). Based on this notion, A. Elleuch and A. Jeribi defined in [8] the structured essential pseudospectrum as follows Definition 1.7. Let A ∈ C(X), B ∈ L(X, Y), C ∈ L(Z, X) and ε > 0.…”