Some notes on the fine spectrum of quintet band matrix operator over $c_{0}$ and $c$

Abstract

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

Keywords

• spectrum Of An Operator
• resolvent set
• perturbed operator
• quintet band matrix
• sequence space

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