Oka Principle on the Maximal Ideal Space of ${\mathbf H^\infty}$

zbMath1398.30034arXiv1707.01482MaRDI QIDQ4636725

Alexander Brudnyi

Publication date: 19 April 2018

Abstract: The classical Grauert and Ramspott theorems constitute the foundation of the Oka principle on Stein spaces. In this paper we establish analogous results on the maximal ideal space $M(H^{i}nfty)$ of the Banach algebra $H^{i}nfty$ of bounded holomorphic functions on the open unit disk $mathbbDsubsetmathbbC$. We illustrate our results by some examples and applications to the theory of operator-valued $H^{i}nfty$ functions.

Full work available at URL: https://arxiv.org/abs/1707.01482

zbMATH Keywords

maximal ideal spacebounded holomorphic functionsOka principlecomplex homogeneous spaceG-bundles

Mathematics Subject Classification ID

Spaces of bounded analytic functions of one complex variable (30H05) Holomorphic bundles and generalizations (32L05)

Related Items (2)

Oka principle on the maximal ideal space of $\boldsymbol {H^\infty }$ ⋮ Topology of the maximal ideal space of \(H^\infty\)

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