Measures of Noncompactness in $\left({\bar{N}}_{{\Delta }^{-}}^q\right)$ Summable Difference Sequence Spaces

Abstract

In the given paper we first introduce ${\bar{N}}_{{\Delta }^{-}}^q$ summable difference sequence spaces and prove some properties of these spaces. We then obtain the necessary and sufficient conditions for infinite matrices $A$ to map these sequence spaces on the spaces $c_0,c$ and ${\ell }_{\infty }$, 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.

16 pages