4 problems

Let $A_\mathbb{R}(\mathbb{D})$ denote the real disc algebra, consisting of functions analytic on $\mathbb{D}$, continuous on $\overline{\mathbb{D}}$, and satisfying the relevant re…

Let $K$ be a compact space and let $A$ be a closed subalgebra of $C(K)$, with the Nevanlinna–Pick property represented by $A\in NP_{\infty}$. Nevanlinna–Pick norm conjecture for un…

Let $R(K)$ denote the uniform algebra of rational functions with poles off a compact set $K\subset\mathbb{C}$. For $x\in K$, write $M_x$ for the maximal ideal of functions in…

Unital uniform-algebra conjecture. If $\|\theta_\alpha\|\leq 1$, then