Abstract
In the peresent paper, by using generalized weighted mean and difference matrix of order $m,$ we introduce the sequence spaces $X(u,v,\Delta^{(m)})$, where $X$ is one of the spaces $\ell_{\infty}$, $c$ or $c_{0}$. Also, we determine the $\alpha$-, $\beta$- and $\gamma$-duals of those spaces and construct their Schauder bases for $X\in\{c,c_{0}\}$. Morever, we give the characterization of the matrix mappings on the spaces $X(u,v,\Delta^{m})$ for $X\in\{\ell_{\infty},c,c_{0}\}.$ Finally, we characterize some classes of compact operators on the spaces $\ell_{\infty}(u,v,\Delta^{m})$ and $c_{0}(u,v,\Delta^{m})$ by using the Hausdorff measure of noncompactness.
Citation
Metin Başarır. Emrah Evren Kara. "On Some Difference Sequence Spaces of Weighted Means and Compact Operators." Ann. Funct. Anal. 2 (2) 114 - 129, 2011. https://doi.org/10.15352/afa/1399900200
Information