A Grauert Type Theorem and Extension of Matrices with Entries in H^{\infty}

摘要

In the paper we prove an extension theorem for matrices with entries inH^{\infty}(U) for U being a Riemann surface of a special type. One of the maincomponents of the proof is a Grauert type theorem for "holomorphic" vectorbundles defined over maximal ideal spaces of certain Banach algebras. The proofis also based on the results of A.Brudnyi "Projections in the Space H^{\infty}and the Corona Theorem for Coverings of Bordered Riemann Surfaces" (see myprevious submissions here).