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On the fine spectrum of the generalized difference operator $$B(r,s)$$ over the sequence spaces $$c_0$$ and $$c$$. (English) Zbl 1098.39013
The fine spectrum [a refinement of the authors’ earlier work in Inf. Sci. 168, 217–224 (2004; Zbl 1085.47041)] of the generalised difference operator $B (r,s)=\left[\begin{matrix} r & 0 & 0 & \dots\\ s & r & 0 & \dots\\ \cdot & \cdot & \cdot & \cdot\\ \cdot & \cdot & \cdot & & \cdot\\ \cdot &\cdot & \cdot &&& \cdot\end{matrix}\right], \quad s\neq 0$ on the sequence $$c_0$$ and $$c_1$$, is obtained.

##### MSC:
 39A70 Difference operators 47B39 Linear difference operators 47A10 Spectrum, resolvent
fine spectrum
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