MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
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.

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Keywords: Matrix transformations, compact operators, measure of noncompactness.

MSC: 40H05, 46A45

Pages:  65--78     

Volume  57 ,  Issue  3$-$4 ,  2005