In this paper, we characterize some operators and matrix transformations in the sequence spaces sα, sα0, sα(c), ℓαp. Moreover, using the Hausdorff measure of noncompactness necessary and sufficient conditions are formulated for a linear operator between the mentioned spaces to be compact. Among other things, some results of Cohen and Dunford are recovered. © 2005 Elsevier Inc. All rights reserved.
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