Compact and Matrix Operators on the Space $\left\vert \overline N_p^{\phi }\right\vert _{k}$

In this paper, determining the operator norm, we give certain characterizations of matrix transformations from space $ \left\vert \overline N_p^{\phi }\right\vert _{k}$, all series summable by absolute weighted mean summability method, to one classical sequence spaces $c_{0},c,l_{\infty }.$ Also, obtain necessary and sufficient conditions for each in these classes be compact establish a number estimates or identities Hausdorff measures noncompactness operators classes.