The Nevanlinna–Pick norm conjecture for uniform algebras

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 uniform algebras. If $A\in NP_{\infty}$ and $A$ is a closed subalgebra of $C(K)$, then $A$ is a $C^{\ast}$-algebra. This is presented as a more specific case of the preceding conjecture. The supplied context gives no resolution of this case; the result for uniform algebras with scattered Gelfand space provides a related positive result.