Holomorphic Banach Vector Bundles on the Maximal Ideal Space of H^\infty and the Operator Corona Problem of Sz.-Nagy

We establish triviality of some holomorphic Banach vector bundles on the maximal ideal space of the Banach algebra of bounded holomorphic functions on the unit disk with pointwise multiplication and supremum norm. We apply the result to the study of the Sz.-Nagy operator corona problem.