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

Year 2021, Volume: 4 Issue: 2, 124 - 133, 01.06.2021

Fadime Gökçe

https://doi.org/10.33401/fujma.882309

Cited By: 2

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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