Fine spectrum of the generalized difference operator Δuv on sequence space l1

In this paper we obtained spectrum and point spectrum of the operator Δuv on l1. The operator Δuv on l1 is defined as Δuvx=(unxn+vn-1xn-1)n=0∞ under certain conditions, where x−1 = 0 and x = (xn) ∈ l1. Further, the results on continuous spectrum, residual spectrum and fine spectrum of the operator Δuv on the sequence space l1 are also derived.