On the fine spectrum of the generalized difference operator B(r,s)B(r,s) over the sequence spaces ℓpℓp and bvp,(1<p<∞)bvp,(1<p<∞)

The main purpose of this paper is to determine the fine spectrum of the operator B(r,s)B(r,s) defined by a band matrix over the sequence spaces ℓpℓp and bvpbvp with 1