On dominating sets for uniform algebra on pseudoconvex domains (Q612262)

Let \(D\) be a bounded domain in \(\mathbb C^n\). Let \(A(D)\) be the uniform algebra on \(D\), i.e.\ the algebra of functions holomorphic in \(D\) and continuous up to the boundary, endowed with the supremum norm. A subset \(E\subset D\) is called a dominating set if for every two function \(f,g\in A(D)\) such that \(|f(z)|\leq|g(z)|\) for all \(z\in E\) then \(\|f\|_\infty\leq\|g\|_\infty\). The paper aims to show a relation between the notion of dominating set and that of Shilov boundary.