Oka principle on the maximal ideal space of 𝐻^{∞}

Brudnyi, A.

doi:10.1090/spmj/1623

Oka principle on the maximal ideal space of $\boldsymbol {H^\infty }$
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by A. Brudnyi

St. Petersburg Math. J. 31 (2020), 769-817

DOI: https://doi.org/10.1090/spmj/1623

Published electronically: September 3, 2020

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Abstract:

The classical Grauert and Ramspott theorems constitute the foundation of the Oka principle on Stein spaces. In this paper, similar results are established on the maximal ideal space $M(H^\infty )$ of the Banach algebra $H^\infty$ of bounded holomorphic functions on the open unit disk $\mathbb {D}\subset \mathbb {C}$. The results are illustrated by some examples and applications to the theory of operator-valued $H^\infty$ functions.

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