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Zbl 1096.47031
Akhmedov, Ali M.; Başar, Feyzi
On the fine spectrum of the Cesàro operator in $c_0$.
(English)
[J] Math. J. Ibaraki Univ. 36, 25-32 (2004). ISSN 1343-3636

The fine spectrum of the Cesàro operator in the sequence space $c_0$ is examined. Although the spectrum of the Cesàro operator in the sequence space $c_0$ was already determined by {\it J.~B.\ Reade} [Bull.\ Lond.\ Math.\ Soc.\ 17, 263--267 (1985; Zbl 0548.47017)] and others, the results of the present paper give a refinement of the previous works. Further, a Mercerian theorem is also stated and proved. Finally, the fine spectrum of the Cesàro operator in the sequence space $c$ is given, without proof.
[Bahman Yousefi (Shiraz)]
MSC 2000:
*47B37 Operators on sequence spaces, etc.
47A10 Spectrum and resolvent of linear operators

Keywords: Cesàro means of order one; sequence space; fine spectrum

Citations: Zbl 0548.47017

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