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
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)
MSC:
47B39 | Linear difference operators |
47A10 | Spectrum, resolvent |
40J05 | Summability in abstract structures |
46A45 | Sequence spaces (including Köthe sequence spaces) |