On the fine spectrum of quadruple band matrix operator over $c_0$ and $c$

Abstract

We give the fine spectrum of the quadruple band matrix operator $Q\left(r,s,t,u\right)$ over $c_0$ and $c$. The matrix $Q\left(r,s,t,u\right)$ generalizes ${\mathrm{\Delta }}^3$, $D\left(r,0,0,s\right)$, $B\left(r,s,t\right)$, ${\mathrm{\Delta }}^2$, $B\left(r,s\right)$, $\mathrm{\Delta }$, right-shift and Zweier matrices, where ${\mathrm{\Delta }}^3$, $B\left(r,s,t\right)$, ${\mathrm{\Delta }}^2$, $B\left(r,s\right)$ and $\mathrm{\Delta }$ are called third-order difference, triple band, second-order difference, double band (generalized difference) and difference matrix, respectively.