Bull. Korean Math. Soc. 2018; 55(5): 1351-1370
Online first article September 5, 2018 Printed September 30, 2018
https://doi.org/10.4134/BKMS.b170775
Copyright © The Korean Mathematical Society.
Fatma Ben Brahim, Aref Jeribi, Bilel Krichen
University of Sfax, University of Sfax, University of Sfax
In the first part of this paper we show that, under some conditions, a polynomially demicompact operator can be demicompact. An example involving the Caputo fractional derivative of order $\alpha $ is provided. Furthermore, we give a refinement of the left and the right Weyl essential spectra of a closed linear operator involving the class of demicompact ones. In the second part of this work we provide some sufficient conditions on the inputs of a closable block operator matrix, with domain consisting of vectors which satisfy certain conditions, to ensure the demicompactness of its closure. Moreover, we apply the obtained results to determine the essential spectra of this operator.
Keywords: matrix operator, demicompact linear operator, Fredholm and semi-Fredholm operators, essential spectra
MSC numbers: 47A53, 47A55, 47A10
2016; 53(3): 681-698
2011; 48(1): 183-195
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