The closed convex hull of the interpolating Blaschke products (Q1385206)

Let \(D\) be the open unit disc in \(\mathbb{C}\). Denote by \(H^\infty\) the space of all bounded analytic functions on \(D\) with uniform norm. A sequence \(\{z_n\} \subset D\) is called interpolating if the mapping \(H^\infty\to \ell^\infty: f\to \{f(z_n)\}\) is onto. A Blaschke product whose zero sequence is an interpolating sequence is called an interpolating Blaschke product. These products play a significant role in the theory of \(H^\infty\). The closed convex hull of the interplating Blaschke products is denoted by \(K\). The result is the following theorem: If \(f\in H^\infty\) and \(\| f\|\leq 10^{-7}\) then \(f\in K\). An interesting and quite technical proof is given.