  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
$f:\Omega\times\Omega\to\CC$ is holomorphic and $f(x,x)=0$ for $x\in\Omega$,
then there is a holomorphic $g:\Omega\times\Omega\to X^*$ with values in the
dual space $X^*$ of $X$ such that $f(x,y)=g(x,y)(x-y)$
