The authors establish some identities or estimates for the Hausdorff measures of noncompactness of certain matrix operators on the difference sequence spaces
where is a strictly increasing sequence of positive real numbers tending to infinity; see [M. Mursaleen and A. K. Noman, Math. Comput. Modelling 52, No. 3–4, 603–617 (2010; Zbl 1201.40003)]. Furthermore, they characterize some classes of compact operators on these spaces.