Compactness via Hausdorff measure of non-compactness and some properties on Tetranacci sequence spaces

The characterization of compact operators on BK-spaces, which is the basis of this research, makes use of the Hausdorff measure of non-compactness. In this study, the compactness criteria of matrix operators defined on BK-spaces $\ell_p(\mathcal{T})$ and $\ell_{\infty}(\mathcal{T})$ which are the domains of the regular infinite Tetranacci matrix obtained by using the Tetranacci number sequence in $\ell_p$ and $\ell_{\infty}$, respectively, are investigated by using Hausdorff measure of non-compactness and some properties of $\ell_p(\mathcal{T})$ are examined.