On the annihilator of a Dolbeault group

Details On the annihilator of a Dolbeault group On the annihilator of a Dolbeault group

2009-10-05

arxiv.org/abs/0910.0737v1

Mathematics

Complex Variables

Scientific paper

We show that any Dolbeault cohomology group $H^{p,q}(D)$, $p\ge0$, $q\ge1$, of an open subset $D$ of a closed finite codimensional complex Hilbert submanifold of $\ell_2$ is either zero or infinite dimensional. We also show that any continuous character of the algebra of holomorphic functions of a closed complex Hilbert submanifold $M$ of $\ell_2$ is induced by evaluation at a point of $M$. Lastly, we prove that any closed split infinite dimensional complex Banach submanifold of $\ell_1$ admits a nowhere critical holomorphic function.

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