On the stable rank of 𝐻^{∞}

Holden, Peter J.

doi:10.1090/S0002-9939-1992-1086329-0

On the stable rank of $H^ \infty$
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Proc. Amer. Math. Soc. 114 (1992), 79-88 Request permission

Abstract:

We prove that if ${f_1},{f_2}$ are corona data and ${f_1}$ is the product of finitely many interpolating Blaschke products, then there exist corona solutions ${g_1},{g_2}$ with $g_1^{ - 1} \in {H^\infty }\left ( D \right )$. This provides a partial result in the direction of proving the stable rank of the algebra of bounded analytic functions on the open unit disc is one.

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