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(r,s,t,u) over c0 and c. The matrix Q(r,s,t,u) generalizes Δ3, D(r,0,0,s), B(r,s,t), Δ2, B(r,s), Δ, right-shift and Zweier matrices, where Δ3, B(r,s,t), Δ2, B(r,s) and Δ are called third-order difference, triple band, second-order difference, double band (generalized difference) and difference matrix, respectively.