Applications of the Hausdorff measure of noncompactness in some sequence spaces of weighted means

Abstract

In the present paper, we establish some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators on some sequence spaces of weighted means. Furthermore, by using the Hausdorff measure of noncompactness, we apply our results to characterize some classes of compact operators on those spaces. © 2010 Elsevier Ltd. All rights reserved.