TY - JOUR
AU - N. Durna
PY - 2018/07/25
Y2 - 2022/10/03
TI - Subdivision of spectra for some lower triangular double-band matrices as operators
on $c_0$
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 70
IS - 7
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1605
AB - 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 determine the approximate point spectrum, the defect spectrum, and the compression spectrum of the operator$\Delta_{a,b}$ in the sequence space $c_0$.
ER -