# MathSciDoc: An Archive for Mathematician ∫

#### K-Theory and Homologymathscidoc:1701.20004

Arkiv for Matematik, 49, (1), 129-148, 2009.4
We prove that every homomorphism $\mathcal{O}^{E}_{\zeta}\rightarrow\mathcal{O}^{F}_{\zeta}$ , with$E$and$F$Banach spaces and ζ∈ℂ^{$m$}, is induced by a $\mathop{\mathrm{Hom}}(E,F)$ -valued holomorphic germ, provided that 1≤$m$<∞. A similar structure theorem is obtained for the homomorphisms of type $\mathcal{O}^{E}_{\zeta}\rightarrow\mathcal{S}_{\zeta}$ , where $\mathcal{S}_{\zeta}$ is a stalk of a coherent sheaf of positive 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.
@inproceedings{vakhid2009homomorphisms,
title={Homomorphisms of infinitely generated analytic sheaves},
author={Vakhid Masagutov},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203629718825997},
booktitle={Arkiv for Matematik},
volume={49},
number={1},
pages={129-148},
year={2009},
}

Vakhid Masagutov. Homomorphisms of infinitely generated analytic sheaves. 2009. Vol. 49. In Arkiv for Matematik. pp.129-148. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203629718825997.