Measures of Noncompactness in (N̅qΔ −) Summable Difference Sequence Spaces.

In this paper we first introduce N̅qΔ − summable difference sequence spaces and prove some properties of these spaces. We then obtain the necessary and sufficient conditions for infinite matrix A to map these sequence spaces on the spaces c, c0 and l∞. Finally, the Hausdorff measure of noncompactness is then used to obtain the necessary and sufficient conditions for the compactness of the linear operators defined on these spaces. [ABSTRACT FROM AUTHOR]