Characterizations of Matrix and Compact Operators on BK Spaces

Authors : Fadime GÖKÇE

Pages : 76-85

Doi:10.32323/ujma.1282831

View : 32 | Download : 34

Publication Date : 2023-07-01

Article Type : Research Paper

Abstract :In the present paper, by estimating operator norms, we give some characterizations of infinite matrix classes $\\leftinsert ignore into journalissuearticles values( \\left\\vert E_{\\mu }^{r}\\right\\vert _{q},\\Lambda\\right); $ and $\\leftinsert ignore into journalissuearticles values( \\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 $c_{0},c,l_{\\infty },l_{q}insert ignore into journalissuearticles values(q\\geq 1);$. 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