Compact operators on the spaces \(a_{0}^{r}(\varDelta)\)and \(a_{c}^{r}(\varDelta)\) (Q2488783)

The present paper is devoted to the study of compact operators acting from the difference sequence spaces \(a_0^r(\Delta)\) and \(a_c^r(\Delta)\), defined recently by \textit{C.~Aydin} and \textit{F.~Başar} [Appl.\ Math.\ Comput.\ 157, No.~3, 677--693 (2004; Zbl 1072.46007)], to the classical spaces \(c_0\), \(c\), \(\ell_\infty\), \(\ell_1\) and \(bv\). In particular, using the Hausdorff measure of noncompactness, the author obtains some conditions on operators from the above classes to be compact.