TY  - JOUR
TI  - On the spectrum of the upper triangular double band matrix $U(a_{0},a_{1},a_{2};b_{0},b_{1},b_{2})$ over the sequence space $c$
AB  - The upper triangular double band matrix $U(a_{0},a_{1},a_{2};b_{0},b_{1},b_{2})$ is defined on a Banach sequence space by $U(a_{0},a_{1},a_{2};b_{0},b_{1},b_{2})(x_{n})=(a_{n}x_{n}+b_{n}x_{n+1})_{n=0}^{infty}$where $a_{x}=a_{y},~b_{x}=b_{y}$ for $xequiv y~(mod3)$. The class of the operator$U(a_{0},a_{1},a_{2};b_{0},b_{1},b_{2})$includes, in particular, the operator $U(r,s)$ when $a_{k}=r$ and $b_{k}=s$ for all $kinmathbb{N}$, with $r,sinmathbb{R}$ and $sneq 0$. Also, it includes the upper difference operator; $a_{k}=1$ and $b_{k}=-1$ for all $kinmathbb{N}$. In this paper, we completely determine the spectrum, the fine spectrum, the approximate point spectrum, the defect spectrum, and the compression spectrum of the operator $U(a_{0},a_{1},a_{2};b_{0},b_{1},b_{2})$ over the sequence space $c$.
AU  - KILIÇ, RABİA
AU  - Durna, Nuh
DO  - 10.31801/cfsuasmas.977593
PY  - 2022
JO  - Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
VL  - 71
IS  - 2
SN  - 1303-5991
SP  - 554
EP  - 565
DB  - TRDizin
UR  - http://search/yayin/detay/1118378
ER  -