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Zbl 1236.47029
Srivastava, P.D.; Kumar, S.
(Kumar, Sudhanshu)
Fine spectrum of the generalized difference operator $\Delta_v $ on sequence space $l_1$. (English)
[J] Thai J. Math. 8, No. 2, 221-233 (2010). ISSN 1686-0209

From the summary: The purpose of this paper is to determine the spectrum and the fine spectrum of the operator $\Delta_v$ on the sequence space $l_1$ defined by $\Delta _vx = (v_nx_n - v_{n - 1} x_{n - 1})^\infty_{n=0}$ with $x_{- 1} = 0$, where $x = (x_n) \in l_1$ and $v = (v_k)$ is either constant or a strictly decreasing sequence of positive real numbers satisfying certain conditions.

MSC 2000:: *47B39 Difference operators (operator theory)
47A10 Spectrum and resolvent of linear operators
46A45 Sequence spaces

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

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