Holomorphic Banach vector bundles on the maximal ideal space of [formula omitted] and the operator corona problem of Sz.-Nagy

Abstract

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