Et, Mikail; Basarir, Metin On some new generalized difference sequence spaces. (English) Zbl 0922.40003 Period. Math. Hung. 35, No. 3, 169-175 (1997). Let \(\omega\) be the space of all complex sequences \(x=(x_k)\). The authors introduce certain generalized difference sequence spaces related to \(\ell_{\infty}\), \(c_0\), \(c\), i.e. to the Banach spaces of bounded, null and convergent sequences, respectively, with the aid of the linear operator \(\Delta^r\), where \(\Delta^r x=(\Delta^r x_k)=(\Delta^{r-1} x_k-\Delta^{r-1} x_{k+1})\), see I. J. Maddox [Math. Proc. Camb. Philos. Soc. 85, 345-350 (1979; Zbl 0417.40007)] and S. Nanda [Bull. Calcutta Math. Soc. 76, 236-240 (1984; Zbl 0588.40009)]. They investigate inclusion relations and Köthe-Toeplitz duals. Here the dual of \(X\) is defined by \(X^{\alpha}=\{a=(a_k)\in \omega\mid \sum_k | a_kx_k| <\infty\) for every \(x\in X\}\). Reviewer: László Tóth (Cluj) Cited in 1 ReviewCited in 40 Documents MSC: 40A05 Convergence and divergence of series and sequences 40C05 Matrix methods for summability 46A45 Sequence spaces (including Köthe sequence spaces) Keywords:difference sequence spaces; Köthe-Toeplitz duals Citations:Zbl 0417.40007; Zbl 0588.40009 PDFBibTeX XMLCite \textit{M. Et} and \textit{M. Basarir}, Period. Math. Hung. 35, No. 3, 169--175 (1997; Zbl 0922.40003) Full Text: DOI