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Fine spectrum of the generalized difference operator \(\Delta_v \) on sequence space \(l_1\). (English) Zbl 1236.47029

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:

47B39 Linear difference operators
47A10 Spectrum, resolvent
46A45 Sequence spaces (including Köthe sequence spaces)
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