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Dergiler / Universal Journal of Mathematics and Applications / 2023 / Cilt: 6 Sayı: 2

Characterizations of Matrix and Compact Operators on BK Spaces

Fadime GÖKÇE
Sayfa
76–85
Yayın Tarihi
2023-07-01
DOI
—
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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 Maddede Bu Makale

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Amaç & Hipotez: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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Temel Bulgular & Veri: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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Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

GÖKÇE, F. (2023). Characterizations of Matrix and Compact Operators on BK Spaces. Universal Journal of Mathematics and Applications, Cilt: 6 Sayı: 2, 76–85. https://ajindex.com/articles/947247

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