Projective free algebras of bounded holomorphic functions on infinitely connected domains

A. Brudnyi

Algebra i analiz, Tome 33 (2021) no. 4, pp. 49-65.

Résumé

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. 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 Čech cohomology group is trivial.

Détail

Keywords: Maximal ideal space, corona problem, projective free ring, Hermite ring, covering dimension, Čech cohomology.

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