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

Alex Brudnyi
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Abstract

In the paper we prove an extension theorem for matrices with entries in H^{\infty}(U) for U being a Riemann surface of a special type. One of the main components of the proof is a Grauert type theorem for "holomorphic" vector bundles defined over maximal ideal spaces of certain Banach algebras. The proof is 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 my previous submissions here).

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Alex Brudnyi. 2001-12-15. A Grauert Type Theorem and Extension of Matrices with Entries in H^{\infty}. https://arxiv.org/abs/math/0112151

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