×

zbMATH — the first resource for mathematics

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
Keywords:
fine spectrum
PDF BibTeX XML Cite
Full Text: DOI