Compact and Matrix Operators on the Space $leftvert overline N_p^{phi }rightvert _{k}$

Abstract

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