Topology of the Maximal Ideal Space of $H^{\infty}$

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dc.creatorBrudnyi, Alexander
dc.date1999-08-30
dc.date.accessioned2026-07-07T05:30:35Z
dc.date.available2026-07-07T05:30:35Z
dc.descriptionWe study the structure of the maximal ideal space $M(H^{\infty})$ of the algebra $H^{\infty}=H^{\infty}(\Di)$ of bounded analytic functions defined on the open unit disk $\Di\subset\Co$. Based on the fact that $dim\ M(H^{\infty})=2$ we prove for $H^{\infty}$ the matrix-valued corona theorem. Our results heavily rely on the topological construction describing maximal ideal spaces of certain algebras of continuous functions defined on the covering spaces of compact manifolds.
dc.identifierhttps://arxiv.org/abs/math/9908168
dc.identifierhttp://arxiv.org/abs/math/9908168
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79034
dc.subjectComplex Variables
dc.subjectFunctional Analysis
dc.subjectPrimary 30D15, Secondary 32F05
dc.titleTopology of the Maximal Ideal Space of $H^{\infty}$
dc.typetext

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