• Title/Summary/Keyword: demicompact operator

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POLYNOMIALLY DEMICOMPACT OPERATORS AND SPECTRAL THEORY FOR OPERATOR MATRICES INVOLVING DEMICOMPACTNESS CLASSES

  • Brahim, Fatma Ben;Jeribi, Aref;Krichen, Bilel
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.5
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    • pp.1351-1370
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    • 2018
  • 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.

CHARACTERIZATION OF RELATIVELY DEMICOMPACT OPERATORS BY MEANS OF MEASURES OF NONCOMPACTNESS

  • Jeribi, Aref;Krichen, Bilel;Salhi, Makrem
    • Journal of the Korean Mathematical Society
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    • v.55 no.4
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    • pp.877-895
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    • 2018
  • 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 FREDHOLM THEORY RESULTS AROUND RELATIVE DEMICOMPACTNESS CONCEPT

  • Chaker, Wajdi;Jeribi, Aref;Krichen, Bilel
    • Communications of the Korean Mathematical Society
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    • v.36 no.2
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    • pp.313-325
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    • 2021
  • 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.