Characterizations of Matrix and Compact Operators on BK Spaces
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 $\ \left\vert E_{\mu }^{r}\right\vert _{q},$ $\left\vert E_{\mu }^{r}\right\vert _{\infty }$ 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.
Keywords:
Absolute summability, Euler matrix, Hausdorff measures of noncompactness, Matrix transformations, Operator norm Sequence spaces,
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- ISSN: 2619-9653
- Başlangıç: 2018
- Yayıncı: Emrah Evren KARA
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Characterizations of Matrix and Compact Operators on BK Spaces