Applications of Measure of Noncompactness in the Series Spaces of Generalized Absolute Cesàro Means

Abstract

In this study, we characterize some matrix transformations from the generalized absolute Cesàro series spaces � , � ( ≥ 1) to the classical sequence spaces ℓ ∞ , c and c 0 . Besides this, we obtain some identities or estimates for the norms of the bounded linear operators corresponding these matrix transformations. Further, by applying the Hausdorff measure of noncompactness, we give the necessary and sufficient conditions for such operators to be compact.