The Shilov Boundary and Peak Points of the Discrete Beurling Algebras on $\mathbb{Z}_+^2$ and $\mathbb{Z}^2$

Abstract

Let $\omega$ be a weight function on $\mathbb{Z}_+^2$ or $\mathbb{Z}^2$. The Gel'fand spaces of the discrete Beurling algebras $l^1(\mathbb{Z}_+^2,\omega)$ and $l^1(\mathbb{Z}^2,\omega)$ are studied in [2]. In this paper, we study their Shilov boundary, peak points and strong boundary points.