The measure of noncompactness of matrix transformations on the spaces cp(Λ) and cınftyp(Λ) ($1

Abstract

We study linear operators between certain sequencespaces X and Y when X is $C^p(\mathrm{\Lambda })$ or$C_{ınfty}^p(\mathrm{\Lambda })$ 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.