Grauert- and Lax–Halmos-type theorems and extension of matrices with entries in <f>H∞</f>

In the paper we prove an extension theorem for matrices with entries in <f>H∞(U)</f> for <f>U</f> 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 on maximal ideal spaces of certain Banach algebras. [Copyright &y& Elsevier]