Stability Criterion for Convolution-Dominated Infinite Matrices

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