Some notes on the fine spectrum of quintet band matrix operator over c0 and c

Abstract

In this work, we determine the fine spectrum of quintet band matrix operator G(r, s, t, u, v) over c0 and c. The quintet band matrix G(r, s, t, u, v) is the general form of the matrices D(r, 0, s, 0, t), ∆4, Q(r, s, t, u), ∆3, D(r, 0, 0, s), B(r, s, t), ∆2, B(r, s), ∆, right shift and Zweier matrices, where ∆4, Q(r, s, t, u), ∆3, B(r, s, t), ∆2, B(r, s) and ∆ are called fourth order difference, quadruple band, third order difference, triple band, second order difference, double band(generalized difference) and difference matrix, respectively.