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http://dx.doi.org/10.4134/JKMS.j170497

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)
Publication Information
Journal of the Korean Mathematical Society / v.55, no.4, 2018 , pp. 877-895 More about this Journal
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.
Keywords
demicompact operator; Fredholm and semi-Fredholm operators; Kuratowskii measure of noncompactness;
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