Subdivision of spectra for some lower triangular double-band matrices as operators on $c_0$

• Date: 2018
• Main Authors: Durna, N., Дурна, Н.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2018
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1605
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

The generalized difference operator $\Delta_{a,b}$ was defined by El-Shabrawy: $\Delta{a,b}x = \Delta_{a,b} (x_n) = (a_nx_n + b_{n-1}x_{n-1})^{\infty}_{n = 0}$ with $x_1 = b_1 = 0$, where $(a_k), (b_k)$ are convergent sequences of nonzero real numbers satisfying certain conditions. We completely det...