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Topology of the Maximal Ideal Space of $H^{\infty}$

Alexander Brudnyi
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Abstract

We study the structure of the maximal ideal space $M(H^{\infty})$ of the algebra $H^{\infty}=H^{\infty}(\Di)$ of bounded analytic functions defined on the open unit disk $\Di\subset\Co$. Based on the fact that $dim\ M(H^{\infty})=2$ we prove for $H^{\infty}$ the matrix-valued corona theorem. Our results heavily rely on the topological construction describing maximal ideal spaces of certain algebras of continuous functions defined on the covering spaces of compact manifolds.

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Alexander Brudnyi. 1999-08-30. Topology of the Maximal Ideal Space of $H^{\infty}$. https://arxiv.org/abs/math/9908168

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