Applications of measure of noncompactness in operators on the spaces sα, s0 α, s(c) α , pα

In this paper, we characterize some operators and matrix transformations in the sequence spaces sα, s0 α, s (c) α , pα . 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.