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

Abstract

In this paper, determining the operator norm, we give certain characterizations of matrix transformations from the space $ \left\vert \overline N_p^{\phi }\right\vert _{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.

Keywords

• Absolute summability
• Compact operator
• Hausdroff meausures of noncompactness
• Matrix transformations
• Operator norm
• Sequence spaces
• Weighted mean

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