On some difference sequence spaces of weighted means and compact operators

Abstract

In the peresent paper, by using generalized weighted mean and difference matrix of order m, we introduce the sequence spaces X(u, v, Δ(m)), where X is one of the spaces ℓ∞, c or c0. Also, we determine the α-, β-and γ-duals of those spaces and construct their Schauder bases for X ∈ (c, c0). Morever, we give the characterization of the matrix mappings on the spaces X(u, v, Δm) for X ∈ (ℓ∞, c, c0). Finally, we characterize some classes of compact operators on the spaces ℓ∞(u, v, Δm) and c0(u, v, Δm) by using the Hausdorff measure of noncompactness. © 2011, Duke University Press. All rights reserved.