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Characterization of relatively demicompact operators by means of measures of noncompactness

Bilel Krichen|Aref Jeribi|Makrem Salhi
대한수학회 (The Korean Mathematical Society)|2018.07|대한수학회지 (Journal of the KMS)|제55권 제4호|pp. 877-895

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참고문헌

키워드

demicompact operatorFredholm and semi-Fredholm operatorsKuratowskii measure of noncompactness
주제분류수학

초록

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.

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.

참고문헌 (20)

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