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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.
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.
The class of $p$-demicompact operators on lattice normed spaces
Imen Ferjani,Bilel Krichen 대한수학회 2024 대한수학회논문집 Vol.39 No.1
In the present paper, we introduce a new class of operators called $p$-demicompact operators between two lattice normed spaces $X$ and $Y$. We study the basic properties of this class. Precisely, we give some conditions under which a $p$-bounded operator be $p$-demicompact. Also, a sufficient condition is given, under which each $p$-demicompact operator has a modulus which is $p$-demicompact. Further, we put in place some properties of this class of operators on lattice normed spaces.
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.
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.
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.