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arXiv · 1905.01532

Projective Freeness of Algebras of Bounded Holomorphic Functions on Infinitely Connected Domains

A. Brudnyi
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Abstract

The algebra $H^\infty(D)$ of bounded holomorphic functions on $D\subset\mathbb C$ is projective free for a wide class of infinitely connected domains. In particular, for such $D$ every rectangular left-invertible matrix with entries in $H^\infty(D)$ can be extended in this class of matrices to an invertible square matrix (the generalization of the corona theorem for $H^\infty(D)$). This follows from a new result on the structure of the maximal ideal space of $H^\infty(D)$ asserting that its covering dimension is $2$ and the second \v{C}ech cohomology group is trivial.

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A. Brudnyi. 2019-05-04. Projective Freeness of Algebras of Bounded Holomorphic Functions on Infinitely Connected Domains. https://arxiv.org/abs/1905.01532

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