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CHARACTERIZATION OF RELATIVELY DEMICOMPACT OPERATORS BY MEANS OF MEASURES OF NONCOMPACTNESS
Jeribi, Aref,Krichen, Bilel,Salhi, Makrem Korean Mathematical Society 2018 대한수학회지 Vol.55 No.4
In this paper, we show that an unbounded $S_0$-demicompact linear operator T with respect to a bounded linear operator $S_0$, acting on a Banach space, can be characterized by the Kuratowskii measure of noncompactness. Moreover, some other quantities related to this measure provide sufficient conditions to the operator T to be $S_0$-demicompact. The obtained results are used to discuss the connection with Fredholm and upper Semi-Fredholm operators.
Characterization of relatively demicompact operators by means of measures of noncompactness
Aref Jeribi,Bilel Krichen,Makrem Salhi 대한수학회 2018 대한수학회지 Vol.55 No.4
In this paper, we show that an unbounded $S_{0}$-demicompact linear operator $T$ with respect to a bounded linear operator $S_{0}$, acting on a Banach space, can be characterized by the Kuratowskii measure of noncompactness. Moreover, some other quantities related to this measure provide sufficient conditions to the operator $T$ to be $S_{0}$-demicompact. The obtained results are used to discuss the connection with Fredholm and upper Semi-Fredholm operators.
Some description of essential structured approximate and defect pseudospectrum
Aymen Ammar,Aref Jeribi,Kamel Mahfoudhi 강원경기수학회 2020 한국수학논문집 Vol.28 No.4
In this paper, we introduce and study the structured essential approximate and defect pseudospectrum of closed, densely defined linear operators in a Banach space. Beside that, we discuss some results of stability and some properties of these essential pseudospectra. Finally, we will apply the results described above to investigate the essential approximate and defect pseudospectra of the following integro-differential transport operator.
SOME FREDHOLM THEORY RESULTS AROUND RELATIVE DEMICOMPACTNESS CONCEPT
Chaker, Wajdi,Jeribi, Aref,Krichen, Bilel Korean Mathematical Society 2021 대한수학회논문집 Vol.36 No.2
In this paper, we provide a characterization of upper semi-Fredholm operators via the relative demicompactness concept. The obtained results are used to investigate the stability of various essential spectra of closed linear operators under perturbations belonging to classes involving demicompact, as well as, relative demicompact operators.
Brahim, Fatma Ben,Jeribi, Aref,Krichen, Bilel Korean Mathematical Society 2018 대한수학회보 Vol.55 No.5
In the first part of this paper we show that, under some conditions, a polynomially demicompact operator can be demicompact. An example involving the Caputo fractional derivative of order ${\alpha}$ is provided. Furthermore, we give a refinement of the left and the right Weyl essential spectra of a closed linear operator involving the class of demicompact ones. In the second part of this work we provide some sufficient conditions on the inputs of a closable block operator matrix, with domain consisting of vectors which satisfy certain conditions, to ensure the demicompactness of its closure. Moreover, we apply the obtained results to determine the essential spectra of this operator.
Fatma Ben Brahim,Aref Jeribi,Bilel Krichen 대한수학회 2018 대한수학회보 Vol.55 No.5
In the first part of this paper we show that, under some conditions, a polynomially demicompact operator can be demicompact. An example involving the Caputo fractional derivative of order $\alpha $ is provided. Furthermore, we give a refinement of the left and the right Weyl essential spectra of a closed linear operator involving the class of demicompact ones. In the second part of this work we provide some sufficient conditions on the inputs of a closable block operator matrix, with domain consisting of vectors which satisfy certain conditions, to ensure the demicompactness of its closure. Moreover, we apply the obtained results to determine the essential spectra of this operator.
ON WEIGHTED AND PSEUDO-WEIGHTED SPECTRA OF BOUNDED OPERATORS
Athmouni, Nassim,Baloudi, Hatem,Jeribi, Aref,Kacem, Ghazi Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.3
In the present paper, we extend the main results of Jeribi in [6] to weighted and pseudo-weighted spectra of operators in a nonseparable Hilbert space ${\mathcal{H}}$. We investigate the characterization, the stability and some properties of these weighted and pseudo-weighted spectra.
SHECHTER SPECTRA AND RELATIVELY DEMICOMPACT LINEAR RELATIONS
Ammar, Aymen,Fakhfakh, Slim,Jeribi, Aref Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.2
In this paper, we denote by L the block matrix linear relation, acting on the Banach space X ⊕ Y, of the form ${\mathcal{L}}=\(\array{A&B\\C&D}\)$, where A, B, C and D are four linear relations with dense domains. We first try to determine the conditions under which a block matrix linear relation becomes a demicompact block matrix linear relation (see Theorems 4.1 and 4.2). Second we study Shechter spectra using demicompact linear relations and relatively demicompact linear relations (see Theorem 5.1).