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On the fine spectrum of the operator over the sequence space $c$. (English) Zbl 1222.40002
Summary: We examine the fine spectrum of the generalized difference operator ${{\Delta }}_{a,b}$ over the sequence space $c$. The boundedness of the operator ${{\Delta }}_{a,b}$ is proved. Also, the norm of this operator is found. The class of the operator ${{\Delta }}_{a,b}$ includes some other special cases such as the generalized difference operator $B\left(r,s\right)$ introduced by B. Altay and F. Başar [Int. J. Math. Math. Sci. 2005, No. 18, 3005–3013 (2005; Zbl 1098.39013)]. Our results not only generalize the corresponding results in the existing literature, but also give results for some more operators.
##### MSC:
 40C05 Matrix methods in summability 47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 40H05 Functional analytic methods in summability 47A10 Spectrum and resolvent of linear operators
##### References:
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