The measure of noncompactness of matrix transformations on the spaces $c^p(\Lambda)$ and $c^p_{ınfty}(\Lambda)$ ($1

Abstract

We study linear operators between certain sequencespaces X and Y when X is $C^{p}(\Lambda)$ or$C^{p}_{ınfty}(\Lambda)$ and Y is one of thespaces: $c$, $c_{0}$, $l_{ınfty}$, $c(\mu)$, $c_{0}(\mu)$, $c_{ınfty}(\mu)$, thatis, we give necessary and sufficient conditions for A to map X intoY and after that necessary and sufficient conditions for A to be acompact operator. These last conditions are obtained by means ofthe Hausdorff measure of noncompactness and given in the form ofconditions for the entries of an infinite matrix A.