An analytic Koszul complex in a Banach space

Abstract

We show that the holomorphic ideal sheaf of a linear section of a pseudoconvex open subset $\Omega$ 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 $x\in \Omega$, then there is a holomorphic $g:\Omega \times \Omega \to X^{\ast }$ with values in the dual space $X^{\ast }$ of $X$ such that $f(x,y)=g(x,y)(x-y)$

14 pages