Hausdorff measure of noncompactness of matrix mappings on certain difference sequence spaces

Abstract

The well-known difference sequence spaces were introduced by Kızmaz [17] in 1981 and have been generalized by many authors uptill now. These spaces were fi rst time extended by Sarıgöl [31] to the sequence spaces$l_{\infty }(\Delta _{q}),$ $c(\Delta _{q})$ or $c_{0}(\Delta _{q})$. The aim of this paper is to establish some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the extended spaces and also to characterize some classes of compact operators by using the Hausdorff measure of noncompactness.