The fine spectrum and the matrix domain of the difference operator \(\Delta\) on the sequence space \(l_{p},\;(0<p<1)\) (Q1014103)

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.