Some topological and geometrical properties of a new difference sequence space (Q535947)

Summary: We introduce the new difference sequence space \(a^r_p(\Delta)\). Further, it is proved that the space \(a^r_p(\Delta)\) is a BK-space including the space \(bv_p\), which is the space of sequences of \(p\)-bounded variation. We also show that the spaces \(a^r_p(\Delta)\) and \(\ell_p\) are linearly isomorphic for \(1\leq p<\infty\). Furthermore, the basis and the \(\alpha\)-, \(\beta\)- and \(\gamma\)-duals of the space \(a^r_p(\Delta)\) are determined. We devote the final section of the paper to examine some geometric properties of the space \(a^r_p(\Delta)\).