Analytic sheaves in Banach spaces

2005/07/26 by Laszlo Lempert, Lempert, Laszlo
Mathematics · #32C35 #32T #46G20 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32C35 #msc:32T #msc:46G20

paper · pdf · doi:10.48550/arxiv.math/0507549

38 pages

arxiv created 2005/07/26 · arxiv updated 2009/12/01

Abstract

We introduce a class of analytic sheaves in a Banach space X, that we call cohesive sheaves. Cohesion is meant to generalize the notion of coherence from finite dimensional analysis. Accordingly, we prove the analog of Cartan's Theorems A and B for cohesive sheaves over pseudoconvex open subsets of X, provided X has an unconditional basis.

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