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J. Korean Math. Soc. 2018; 55(4): 877-895

Online first article March 14, 2018      Printed July 1, 2018

https://doi.org/10.4134/JKMS.j170497

Copyright © The Korean Mathematical Society.

Characterization of relatively demicompact operators by means of measures of noncompactness

Aref Jeribi, Bilel Krichen, Makrem Salhi

University of Sfax, University of Sfax, University of Sfax

Abstract

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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

MSC numbers: 47A55, 47A53, 47H08

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