Domain of q-Cesàro matrix in Hahn sequence space hd and the space bv of the sequences of bounded variation

Abstract

Let hd = n f = (fk) ? ? : P k dk| fk ? fk+1| < ? o ? c0, where d = (dk) is an unbounded and monotonic increasing sequence of positive reals. We study the matrix domains hd(Cq) = (hd)Cq and bv(Cq)=(bv)Cq, where Cq is the q-Ces?ro matrix, 0 < q < 1. Apart from the inclusion relations and Schauder basis, we compute ?-, ?- and ?-duals of the spaces hd(Cq) and bv(Cq). We state and prove theorems concerning characterization of matrix classes from the spaces hd(Cq) and bv(Cq) to any one of the space ??, c, c0 or ?1. Finally, we obtain certain identities concerning characterization of compact operators using Hausdorff measure of non-compactness in the space hd(Cq).