Compactness of Matrix Operators on the Banach Space $\ell_p(T)$

Abstract

In this study, by using the Hausdorff measure of non-compactness, we obtain the necessary and sufficient conditions for certain matrix operators on the spaces $\ell_p(T)$ and $\ell_\infty(T)$ to be compact, where $1\leq p<\infty$.