Homomorphisms of infinitely generated analytic sheaves

2008/11/12 by Vakhid Masagutov, Masagutov, Vakhid
Mathematics · #13C15 #32C35 #32L10 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:13C15 #msc:32C35 #msc:32L10

paper · pdf · doi:10.48550/arxiv.0811.1978

arxiv created 2008/11/12 · arxiv updated 2009/12/01

Abstract

We prove that every homomorphism O^E_ζ\toO^F_ζ, with E and F Banach spaces and ζ∈ℂ^m, is induced by a \mathopHom(E,F)-valued holomorphic germ, provided that 1≤ m<∞. A similar structure theorem is obtained for the homomorphisms of type O^E_ζ\toS_ζ, where S_ζ is a stalk of a coherent sheaf of positive \mathfrakm_ζ-depth. We later extend these results to sheaf homomorphisms, obtaining a condition on coherent sheaves which guarantees the sheaf to be equipped with a unique analytic structure in the sense of Lempert-Patyi.

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