Infinite dimensional universal subspaces generated by Blaschke products

Let $H^\infty$ be the Banach algebra of all bounded analytic functions in the unit disk $\mathbb{D}$. A function $f\in H^\infty$ is said to be universal with respect to the sequence $(\frac{z+z_n}{1+\overline{z}_nz})_n$ of noneuclidian translates, if the set $\{f(\frac{z+z_n}{1+\overline {z}_nz}):n\in\mathbb{N}\}$ is locally uniformly dense in the set of all holomorphic functions bounded by $\vert\vert f\vert\vert _\infty$. We show that for any sequence of points $(z_n)$ in $\mathbb{D}$ tending to the boundary there exists a closed subspace of $H^\infty$, topologically generated by Blaschke products, and linear isometric to $\ell^1$, such that all of its elements $f$ are universal with respect to noneuclidian translates. The proof is based on certain interpolation problems in the corona of $H^\infty$. Results on cyclicity of composition operators in $H^2$ are deduced.