Cesaro Difference Sequence Spaces and its Dual

Abstract

The difference sequence spaces $c_{0}(\Delta), c(\Delta)$ and $\ell_{\infty}(\Delta)$ were introduced by Kizmaz [4]. Et [8] introduced the Cesàro difference sequence spaces $X_{p}\left(\Delta^{m}\right)(1 \leq p<\infty), X_{\infty}\left(\Delta^{m}\right)$ and determine their generalized Köthe-Toeplitz duals and some of the related matrix transformations. In this paper, we compute $\eta$-duals of $C_{1}(\Delta), C_{1}\left(\Delta^{2}\right)$ and $X_{\infty}\left(\Delta^{2}\right)$, the matrix classes $(C_{1}(\Delta), \ell_{\infty})$, $(C_{1}(\Delta), c ; p)$, $(C_{1}(\Delta), C_{0})$, $(C_{1}(\Delta^{2}), \ell_{\infty})$, $(C_{1}(\Delta^{2}), c)$, and $\left(C_{1}\left(\Delta^{2}\right), c_{0}\right)$ are also characterized.