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.
Keywords:oka principle, maximal ideal space of $H^\infty$, Grauert theorem, Ramspott theorem.
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