Abstract
This paper concerns the spectrum and the fine spectrum of the discrete generalized Cesàro operator \(C_{t}\), where \(0\le t<1\), on Banach sequence spaces close to \(\ell ^{1}\) and \(\ell ^{\infty }\). We derive some compactness results for the operator \(C_{t}\) to describe the spectrum. Our technique involves standard operator theory and summability theory.
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08 March 2020
In the original article, in Theorem 7.4 (in all statements from (1) to (9)): the symbol <Emphasis Type="Italic">C</Emphasis><Subscript>0</Subscript> should be replaced by bv.
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Acknowledgements
The authors are very indebted to the editor and an anonymous referee for a careful reading of the original manuscript and a number of valuable suggestions that helped improve the presentation of this article. The paper presents results of the Project Grant-in-Aid for Scientific Research (C) (16K05209), funded by the Japan Society for the Promotion of Science. The first author is supported by Department of Mathematics Analysis and the Theory of functions, Peoples’ Friendship University of Russia, Moscow, Russia.
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Communicated by Gerald Teschl.
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Sawano, Y., El-Shabrawy, S.R. Fine spectra of the discrete generalized Cesàro operator on Banach sequence spaces. Monatsh Math 192, 185–224 (2020). https://doi.org/10.1007/s00605-020-01376-w
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DOI: https://doi.org/10.1007/s00605-020-01376-w