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Zbl 0691.40004
Okutoyi, J.I.
On the spectrum of $C\sb 1$ as an operator on $bv\sb 0$.
(English)
[J] J. Aust. Math. Soc., Ser. A 48, No.1, 79-86 (1990). ISSN 0263-6115

Summary: {\it J. Reade} [Bull. Lond. Math. Soc. 17, 263-267 (1985; Zbl 0548.47017)] determined the spectrum of $C\sb 1$ regarded as an operator on the space $c\sb 0$ of all null sequences normed by $\Vert x\Vert =\sup\sb{n\ge 0}\vert x\sb n\vert.$ It is the purpose of this paper to determine the spectrum of $C\sb 1$ regarded as an operator on the space $bv\sb 0$ of all sequences x such that $x\sb k\to 0$ as $k\to \infty$ and $\Vert x\Vert =\sum\sp{\infty}\sb{k=0}\vert x\sb{k+1}-x\sb k\vert <\infty.$
MSC 2000:
*40F05 Special cases of summability
47A10 Spectrum and resolvent of linear operators

Citations: Zbl 0548.47017

Cited in: Zbl 0999.47002

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