General Mathematics, Vol. 7, pp. 85-92, 1999
Abstract:
In a series of papers, the authors has previously investigated the spectra and fine spectra for discrete Ces\`aro operators, considered as bounded operators over various sequence spaces. In this paper I examined the fine spectra of discrete Ces\`aro operators as operator over $bv_{0}$, the spaces of null sequences of bounded variation: \[ \sigma_{r}(C_{1},bv_{0})=\{\lambda :\lambda I-C_{1}\ \mbox{injective and}\ \overline{(\lambda I-C_{1})(bv_{0})}\not= bv_{0}\}, \] \[ \sigma_{c}(C_{1},bv_{0})=\{\lambda :\lambda I-C_{1}\ \mbox{injective, nesurjective and}\ \overline{(\lambda I-C_{1})(bv_{0})}= bv_{0}\}. \] \hspace*{0.6cm} In \cite{b3} the author investigated the spectrum and punctual spectrum for $C_{1}:bv_{0}\ri bv_{0}$.Full text of the article: