On the fine spectrum of the operator Q(r,s,t,u) over ℓp and bvp, 1<p<∞

Abstract

We specify the fine spectrum of the quadruple band matrix operator Q(r,s,t,u) over the sequence spaces ℓp and bvp, where 1<p<∞. The quadruple band matrix Q(r,s,t,u) is the general state of 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.