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.
📌 3 Key Takeaways
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Objective & Hypothesis: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.
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Key Findings & Data: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.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Absolute summability · Compact operator · Hausdroff meausures of noncompactness
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.
GÖKÇE, F. (2021). Compact and Matrix Operators on the Space $\left\vert \overline N_p^{\phi }\right\vert _{k}$. Fundamental Journal of Mathematics and Applications, Cilt: 4 Sayı: 2, 124–133. https://ajindex.com/articles/905703
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