Holomorphic Banach vector bundles on the maximal ideal space of H∞H∞ and the operator corona problem of Sz.-Nagy

We establish triviality of some holomorphic Banach vector bundles on the maximal ideal space M(H∞)M(H∞) of the Banach algebra H∞H∞ of bounded holomorphic functions on the unit disc D⊂CD⊂C with pointwise multiplication and supremum norm. We apply the result to the study of the Sz.-Nagy operator corona problem.