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 < ∞)

Abstract

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 ?v is ?v x = ?v (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 ?v and modified of the operator ?v on the sequence spaces c and ????p (1 < p < ?).