Infinite dimensional universal subspaces generated by Blaschke products

Let be the Banach algebra of all bounded analytic functions in the unit disk . A function is said to be universal with respect to the sequence of noneuclidian translates, if the set is locally uniformly dense in the set of all holomorphic functions bounded by . We show that for any sequence of points in tending to the boundary there exists a closed subspace of , topologically generated by Blaschke products, and linear isometric to , such that all of its elements are universal with respect to noneuclidian translates. The proof is based on certain interpolation problems in the corona of . Results on cyclicity of composition operators in are deduced.