  In this paper, we introduce a class of infinite matrices related to the
Beurling algebra of periodic functions, and we show that it is an
inverse-closed subalgebra of ${\mathcal B}(\ell^q_w)$, the algebra of all
bounded linear operators on the weight sequence space $\ell^q_w$, for any $1\le
q<\infty$ and any discrete Muckenhoupt $A_q$-weight $w$.
