Interpolating Blaschke products generate \(H^ \infty\) (Q1814770)

A Blaschke product \(B(z)\) with zeros \(\{z_n\}\) is called an interpolating Blaschke product if there exists a number \(\delta_B>0\) such that, for each \(n\), \((1-|z |^2) B'(z)\geq \delta_B\). As the title of this paper indicates, the authors prove that the space \(H^\infty\) is the closed linear span of the collection of all interpolating Blaschke products. The proof uses some ideas in a paper due to \textit{D. E. Marshall} and \textit{A. Straye} [Pac. J. Math. 173, No. 2, 491-499 (1996; Zbl 0855.30028)], in which a special case of the present result was proved.