Analytic cohomology in a Banach space

2005/07/25 by Imre Patyi, Patyi, Imre
Mathematics · #32L10 #Advanced Banach Space Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.CV #msc:32L10

paper · pdf · doi:10.48550/arxiv.math/0507520

35 pages

arxiv created 2005/07/25 · openalex publication_date 2005/07/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Among other things, we show that the ideal sheaf of a complex Hilbert submanifold of a pseudoconvex open subset of Hilbert space is acyclic over the ambient pseudoconvex open set. We also prove a vanishing theorem for a fairly general class of analytic sheaves over pseudoconvex open sets of a large class of Banach spaces. Some applications are also given.

Related

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• Analytic sheaves in Banach spaces
• Analytic cohomology groups of infinite dimensional complex manifolds
• An embedding theorem for pseudoconvex domains in Banach spaces
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