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

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Fundamental Journal of Mathematics and Applications
Volume:4 Issue:2
Compact and Matrix Operators on the Space $leftvert overline N_p^{phi }rightvert _{k}$

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

Pages : 124-133

View : 60 | Download : 17

Publication Date : 2021-06-01

Article Type : Research Paper

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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