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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.