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

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