On the fine spectrum of the operator B(r,s,t)B(r,s,t) over c0c0 and cc

We determine the fine spectrum of the operator B(r,s,t)B(r,s,t) defined by a triple-band matrix over the sequence spaces c0c0 and cc. This generalizes the spectrum of the second-order difference operator Δ2 and includes some other special cases such as the generalized difference operator B(r,s)B(r,s) of [B. Altay, F. Başar, On the fine spectrum of the generalized difference operator B(r,s)B(r,s) over the sequence spaces c0c0 and cc, Internat. J. Math. Math. Sci. 18 (2005) 3005–3013], the difference operator Δ of [B. Altay, F. Başar, On the fine spectrum of the difference operator on c0c0 and cc, Inform. Sci. 168 (2004) 217–224], the right shift and Zweier matrices.