maximal ideal space of $H^\infty$ — 1 articles found.

Grauert and Ramspott Type Theorems on the Maximal Ideal Space of ${\mathbf H^\infty}$

C. R. Math. Rep. Acad. Sci. Canada Vol. 39 (4) 2017, pp. 116-132
Vol.39 (4) 2017
Alexander Brudnyi Details
(Received: 2017-07-03 , Revised: 2017-07-06 )
(Received: 2017-07-03 , Revised: 2017-07-06 )

Alexander Brudnyi,Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4;


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 \(M(H^\infty)\) of the Banach algebra \(H^\infty\) of bounded holomorphic functions on the open unit disk \({\mathbb D}\subset{\mathbb C}\). We illustrate our results by some examples and applications to the theory of operator-valued \(H^\infty\) functions.

Les théorèmes classiques de Grauert et Ramspott constituent la base du principe d’Oka par rapport aux espaces Stein. Dans cet article, nous démontrons des résultats analogues sur l’espace idéal maximal \(M(H^\infty)\) de l’algèbre de Banach \(H^\infty\) des fonctions holomorphes bornées sur une disque d’unité ouverte \({\mathbb D} \subset{\mathbb C}\). Nous présentons nos résultats avec des exemples et des applications à la théorie des fonctions \(H^\infty\) évaluées par l’opérateur.

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

AMS Subject Classification: Spaces and algebras of analytic functions, Holomorphic bundles and generalizations 30H05, 32L05

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