Open Access
Translator Disclaimer
April 2011 Homomorphisms of infinitely generated analytic sheaves
Vakhid Masagutov
Author Affiliations +
Ark. Mat. 49(1): 129-148 (April 2011). DOI: 10.1007/s11512-010-0129-x

Abstract

We prove that every homomorphism $\mathcal{O}^{E}_{\zeta}\rightarrow\mathcal{O}^{F}_{\zeta}$, with E and F Banach spaces and ζ∈ℂm, 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.

Funding Statement

Research partially supported by NSF grant DMS0700281 and the Mittag-Leffler Institute, Stockholm. I am grateful to both organizations, and I, particularly, would like to express my gratitude to the Mittag-Leffler Institute for their hospitality during my research leading to this paper. I am indebted to Professor Lempert for his guidance and for proposing questions that motivated this work. I am especially grateful for his suggestions and critical remarks that were invaluable at the research and writing phases. Lastly, I would like to thank the anonymous referee for devoting the time and effort to thoroughly review the manuscript and for suggesting numerous improvements.

Citation

Download Citation

Vakhid Masagutov. "Homomorphisms of infinitely generated analytic sheaves." Ark. Mat. 49 (1) 129 - 148, April 2011. https://doi.org/10.1007/s11512-010-0129-x

Information

Received: 27 April 2009; Revised: 17 March 2010; Published: April 2011
First available in Project Euclid: 31 January 2017

zbMATH: 1216.32003
MathSciNet: MR2784261
Digital Object Identifier: 10.1007/s11512-010-0129-x

Rights: 2010 © Institut Mittag-Leffler

JOURNAL ARTICLE
20 PAGES


SHARE
Vol.49 • No. 1 • April 2011
Back to Top