Vanishing cohomology for holomorphic vector bundles in a Banach setting
type: Item
instance of: scholarly article
title: Vanishing cohomology for holomorphic vector bundles in a Banach setting
zbMATH Open document ID: 1089.32011
author: László Lempert
published in: The Asian Journal of Mathematics
publication date: 2005-03-21T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ajm/1087840909
review text: The author proves: for a complex Banach space \(X\) with countable unconditional basis, all open pseudoconvex \(\Omega\subset X\), and for a locally trivial holomorphic Banach bundle \(E\to \Omega\), the cohomology groups \(H^q(\Omega,E)\) vanish for \(q\geq 1\). More generally, the same vanishing theorem is established for \(X\) with a Schauder basis and a certain approximation hypothesis (which is fulfilled in the case above). Also, an infinite dimensional extension of H. Cartan's Theorem A is given.
reviewed by: Alfred Aeppli
Mathematics Subject Classification ID: 32K99
Mathematics Subject Classification ID: 46G20
Mathematics Subject Classification ID: 32E99
zbMATH DE Number: 2148242
zbMATH Keywords: holomorphic vector bundles
zbMATH Keywords: Banach spaces
MaRDI profile type: Publication
OpenAlex ID: W2162835151
DOI: 10.4310/AJM.2004.V8.N1.A7
description: scientific article; zbMATH DE number 2148242