Stability Criterion for Convolution-Dominated Infinite Matrices

Let $\ell^p$ be the space of all $p$-summable sequences on $\mathbb{Z}$. An infinite matrix is said to have $\ell^p$-stability if it is bounded and has bounded inverse on $\ell^p$. In this paper, a practical criterion is established for the $\ell^p$-stability of convolution-dominated infinite matrices.