On the fine spectrum of the operator Δa,bΔa,b over the sequence space cc

In this paper we examine the fine spectrum of the generalized difference operator Δa,bΔa,b over the sequence space cc. The boundedness of the operator Δa,bΔa,b has been proved. Also, the norm of this operator has been found. The class of the operator Δa,bΔa,b includes some other special cases such as the generalized difference operator B(r,s)B(r,s) introduced by Altay and Başar in 2005. Our results not only generalize the corresponding results in the existing literature, but also give results for some more operators.