Also, we obtain necessary and sufficient conditions for each matrix in these classes to be compact establishing their identities or estimates for the Hausdorff measures of noncompactness.
📌 3 Key Takeaways
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Objective & Hypothesis:In the present paper, by estimating operator norms, we give some characterizations of infinite matrix classes $\left( \left\vert E_{\mu }^{r}\right\vert _{q},\Lambda\right) $ and $\left( \left\vert E_{\mu }^{r}\right\vert _{\infty },\Lambda\right) $, where the absolute spaces $\ \left\vert E_{\mu }^{r}\right\vert _{q},$ $\left\vert E_{\mu }^{r}\right\vert _{\infty }$ have been recently studied by G\"{o}k\c{c}e and Sar{\i }g\"{o}l \cite{GS2019c} and $\Lambda$ is one of the well-known spaces $c_{0},c,l_{\infty },l_{q}(q\geq 1)$.
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Key Findings & Data:In the present paper, by estimating operator norms, we give some characterizations of infinite matrix classes $\left( \left\vert E_{\mu }^{r}\right\vert _{q},\Lambda\right) $ and $\left( \left\vert E_{\mu }^{r}\right\vert _{\infty },\Lambda\right) $, where the absolute spaces $\ \left\vert E_{\mu }^{r}\right\vert _{q},$ $\left\vert E_{\mu }^{r}\right\vert _{\infty }$ have been recently studied by G\"{o}k\c{c}e and Sar{\i }g\"{o}l \cite{GS2019c} and $\Lambda$ is one of the well-known spaces $c_{0},c,l_{\infty },l_{q}(q\geq 1)$.
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Conclusion & Impact:Also, we obtain necessary and sufficient conditions for each matrix in these classes to be compact establishing their identities or estimates for the Hausdorff measures of noncompactness.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Absolute summability · Euler matrix · Hausdorff measures of noncompactness
Abstract
In the present paper, by estimating operator norms, we give some characterizations of infinite matrix classes $\left( \left\vert E_{\mu }^{r}\right\vert _{q},\Lambda\right) $ and $\left( \left\vert E_{\mu }^{r}\right\vert _{\infty },\Lambda\right) $, where the absolute spaces $\ \left\vert E_{\mu }^{r}\right\vert _{q},$ $\left\vert E_{\mu }^{r}\right\vert _{\infty }$ have been recently studied by G\"{o}k\c{c}e and Sar{\i }g\"{o}l \cite{GS2019c} and $\Lambda$ is one of the well-known spaces $c_{0},c,l_{\infty },l_{q}(q\geq 1)$. Also, we obtain necessary and sufficient conditions for each matrix in these classes to be compact establishing their identities or estimates for the Hausdorff measures of noncompactness.
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