Altay, Bilâl; Başar, Feyzi The fine spectrum and the matrix domain of the difference operator \(\Delta\) on the sequence space \(l_{p},\;(0<p<1)\). (English) Zbl 1173.47021 Commun. Math. Anal. 2, No. 2, 1-11 (2007). The authors study the fine spectrum and the matrix domain \(bv_{p}\), \(0<p<1\), of the difference operator \(\Delta\) in the sequence space \(\ell_{p}\). They prove that \(bv_{p}\) is a \(p\)-normed space and is linearly isomorphic to the space \(\ell _{p}\). Finally, the \(\beta\)- and \(\gamma\)-duals of the space \(bv_{p}\) are computed and the characterization of the matrix mappings from the space \(bv_{p}\) into \(\mu\) and from \(\mu\) into \(bv_{p}\) is given, where \(\mu\) is any given sequence space. Reviewer: Bilender P. Allahverdiev (Isparta) Cited in 72 Documents MSC: 47B39 Linear difference operators 47A10 Spectrum, resolvent 40J05 Summability in abstract structures 46A45 Sequence spaces (including Köthe sequence spaces) Keywords:spectrum of a linear operator; difference sequences; matrix mappings PDFBibTeX XMLCite \textit{B. Altay} and \textit{F. Başar}, Commun. Math. Anal. 2, No. 2, 1--11 (2007; Zbl 1173.47021)