We obtain some topological results of the sequence spaces Δm(X), where Δm(X)={x=(xk):(Δmxk)∈X}, (m∈ℕ), 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.