An analytic Koszul complex in a Banach space

Imre Patyi

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An analytic Koszul complex in a Banach space

Imre Patyi

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Abstract

We show that the holomorphic ideal sheaf of a linear section of a pseudoconvex open subset $Ω$ of, say, a Hilbert space $X=\ell_2$ is acyclic. We also prove an analog of Hefer's lemma, i.e., if $f:Ω\timesΩ\to\CC$ is holomorphic and $f(x,x)=0$ for $x\inΩ$, then there is a holomorphic $g:Ω\timesΩ\to X^*$ with values in the dual space $X^*$ of $X$ such that $f(x,y)=g(x,y)(x-y)$

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BibTeX RIS

Imre Patyi. 2005-09-23. An analytic Koszul complex in a Banach space. https://arxiv.org/abs/math/0509556

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