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CHARACTERIZATION OF RELATIVELY DEMICOMPACT OPERATORS BY MEANS OF MEASURES OF NONCOMPACTNESS

  • Jeribi, Aref (Department of Mathematics Faculty of Sciences of Sfax University of Sfax) ;
  • Krichen, Bilel (Department of Mathematics Faculty of Sciences of Sfax University of Sfax) ;
  • Salhi, Makrem (Department of Mathematics Faculty of Sciences of Sfax University of Sfax)
  • Received : 2017.07.26
  • Accepted : 2018.01.16
  • Published : 2018.07.01

Abstract

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.

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