Partition of the spectra for the lower triangular double band matrix as generalized difference operator Δv over the sequence spaces c and lp (1 < p < ∞)
Let the sequence (vk) is assumed to be either constant or strictly decreasing sequence of positive real numbers satisfying limk→∞ vk = L > 0 and supk vk ≤ 2L. Then the generalized difference operator Δv is Δv x = Δv (xn) = (vnxn − vn−1xn−1)∞ n=0 with x−1 = v−1 = 0. The aim of this paper is to obtain the approximate point spectrum, the defect spectrum and the compression spectrum of the operator Δv and modified of the operator Δv on the sequence spaces c and ????p (1 < p < ∞).