Characterizations of Matrix and Compact Operators on BK Spaces
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 }...
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| Format: | Article |
| Language: | English |
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Emrah Evren KARA
2023-07-01
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| Series: | Universal Journal of Mathematics and Applications |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/3082643 |
| _version_ | 1797354907366326272 |
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| author | Fadime Gökçe |
| author_facet | Fadime Gökçe |
| author_sort | Fadime Gökçe |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T13:56:34Z |
| format | Article |
| id | doaj.art-e61644ecb0d24494a31e21751b9fe31d |
| institution | Directory Open Access Journal |
| issn | 2619-9653 |
| language | English |
| last_indexed | 2024-03-08T13:56:34Z |
| publishDate | 2023-07-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Universal Journal of Mathematics and Applications |
| spelling | doaj.art-e61644ecb0d24494a31e21751b9fe31d2024-01-15T15:12:55ZengEmrah Evren KARAUniversal Journal of Mathematics and Applications2619-96532023-07-0162768510.32323/ujma.12828311225Characterizations of Matrix and Compact Operators on BK SpacesFadime Gökçe0PAMUKKALE ÜNİVERSİTESİIn 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.https://dergipark.org.tr/tr/download/article-file/3082643absolute summabilityeuler matrixhausdorff measures of noncompactnessmatrix transformationsoperator normsequence spaces |
| spellingShingle | Fadime Gökçe Characterizations of Matrix and Compact Operators on BK Spaces Universal Journal of Mathematics and Applications absolute summability euler matrix hausdorff measures of noncompactness matrix transformations operator norm sequence spaces |
| title | Characterizations of Matrix and Compact Operators on BK Spaces |
| title_full | Characterizations of Matrix and Compact Operators on BK Spaces |
| title_fullStr | Characterizations of Matrix and Compact Operators on BK Spaces |
| title_full_unstemmed | Characterizations of Matrix and Compact Operators on BK Spaces |
| title_short | Characterizations of Matrix and Compact Operators on BK Spaces |
| title_sort | characterizations of matrix and compact operators on bk spaces |
| topic | absolute summability euler matrix hausdorff measures of noncompactness matrix transformations operator norm sequence spaces |
| url | https://dergipark.org.tr/tr/download/article-file/3082643 |
| work_keys_str_mv | AT fadimegokce characterizationsofmatrixandcompactoperatorsonbkspaces |