Compactness of matrix operators on some new difference sequence spaces

Abstract

The difference sequence spaces c 0 λ ( Δ ) and ℓ ∞ λ ( Δ ) have recently been introduced by Mursaleen and Noman (2010) [M. Mursaleen, A.K. Noman, On some new difference sequence spaces of non-absolute type, Math. Comput. Modelling 52 (3–4) (2010) 603–617]. In the present paper, we establish some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the spaces c 0 λ ( Δ ) and ℓ ∞ λ ( Δ ) . Further, by using the Hausdorff measure of noncompactness, we characterize some classes of compact operators on these spaces.