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Zbl 1222.40002
Akhmedov, A.M.; El-Shabrawy, S.R.
On the fine spectrum of the operator over the sequence space $c$. (English)
[J] Comput. Math. Appl. 61, No. 10, 2994-3002 (2011). ISSN 0898-1221

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 $B(r,s)$ introduced by {\it B. Altay} and {\it 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 2000:: *40C05 Matrix methods in summability
47B37 Operators on sequence spaces, etc.
40H05 Functional analytic methods in summability
47A10 Spectrum and resolvent of linear operators

Keywords: spectrum of an operator; generalized difference operator; sequence space

Citations: Zbl 1098.39013

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Zentralblatt MATH Berlin [Germany]