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