Four New Sequence Spaces Obtained from the Domain of Quadruple Band Matrix Operator

Abstract

In this work, we construct the sequence spaces $c_{0}(Q)$, $c(Q)$, $\ell_{\infty}(Q)$ and $\ell_{p}(Q)$ derived by the domain of quadruple band matrix, which generalizes the matrices $\Delta^{3}$, $B(r,s,t)$, $\Delta^{2}$, $B(r,s)$, $\Delta$, where $\Delta^{3}$, $B(r,s,t)$, $\Delta^{2}$, $B(r,s)$ and $\Delta$ are called third order difference, triple band, second order difference, double band and difference matrix, in turn. Also, we investigate some topological properties and some inclusion relations related to those spaces. Furthermore, we give the Schauder basis of the spaces $c_{0}(Q)$, $c(Q)$ and $\ell_{p}(Q)$, and determine $\alpha-\beta-$ and $\gamma-$duals of those spaces. Lastly, we characterize some matrix classes related to some of those spaces.