Stability Criterion for Convolution-Dominated Infinite Matrices

Abstract

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.