- Universal Journal of Mathematics and Applications
- Vol: 6 Issue: 2
- Characterizations of Matrix and Compact Operators on BK Spaces
Characterizations of Matrix and Compact Operators on BK Spaces
Authors : Fadime Gökçe
Pages : 76-85
Doi:10.32323/ujma.1282831
View : 31 | Download : 33
Publication Date : 2023-07-01
Article Type : Research Article
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.Keywords : Absolute summability, Euler matrix, Hausdorff measures of noncompactness, Matrix transformations, Operator norm, Sequence spaces