TY - JOUR AU - Durna, Nuh PY - 2020/02/04 Y2 - 2024/03/28 TI - 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 < ∞) JF - Proyecciones (Antofagasta, On line) JA - Proyecciones (Antofagasta, On line) VL - 39 IS - 1 SE - DO - 10.22199/issn.0717-6279-2020-01-0004 UR - https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3975 SP - 51-71 AB - <p><em>Let the sequence (v<sub>k</sub>) is assumed to be either constant or strictly decreasing sequence of positive real numbers satisfying lim<sub>k→∞</sub> v<sub>k</sub> = L &gt; 0 and sup<sub>k</sub> v<sub>k</sub> ≤ 2L. Then the generalized difference operator Δ<sub>v</sub> is Δ<sub>v</sub> x = Δ<sub>v</sub> (x<sub>n</sub>) = (v<sub>n</sub>x<sub>n</sub> − v<sub>n−1</sub>x<sub>n−1</sub>)<sup>∞</sup> <sub>n=0</sub> with x<sub>−1</sub> = v<sub>−1</sub> = 0. The aim of this paper is to obtain the approximate point spectrum, the defect spectrum and the compression spectrum of the operator Δ<sub>v</sub> and modified of the operator Δ<sub>v</sub> on the sequence spaces c and </em><em>l</em><em><sub>p</sub></em><em> (1 &lt; p &lt; ∞).</em></p> ER -