Srivastava, P. D.; Kumar, S. Fine spectrum of the generalized difference operator \(\Delta_v \) on sequence space \(l_1\). (English) Zbl 1236.47029 Thai J. Math. 8, No. 2, 221-233 (2010). 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. Cited in 1 ReviewCited in 26 Documents MSC: 47B39 Linear difference operators 47A10 Spectrum, resolvent 46A45 Sequence spaces (including Köthe sequence spaces) Keywords:spectrum of an operator; generalized difference operator; sequence spaces PDFBibTeX XMLCite \textit{P. D. Srivastava} and \textit{S. Kumar}, Thai J. Math. 8, No. 2, 221--233 (2010; Zbl 1236.47029)