Abstract

We obtain some topological results of the sequence spaces Δm(X), where Δm(X)={x=(xk):(Δmxk)X},(m), and X is any sequence space. We compute the pα-, pβ-, and pγ-duals of l,c, and c0 and we investigate the N-(or null) dual of the sequence spaces Δm(l),Δm(c), and Δm(c0). Also we show that any matrix map from Δm(l) into a BK-space which does not contain any subspace isomorphic to Δm(l) is compact.