| The measure of noncompactness of matrix transformations on the spaces $c^p(\Lambda)$ and $c^p_{\infty}(\Lambda)$ ($1 |
| Ivana Stanojević |
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.
|
Keywords: Matrix transformations, compact operators, measure of noncompactness. |
MSC: 40H05, 46A45 |
Pages: 65$-$78 |
Volume 57 , Issue 3$-$4 , 2005 |
