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On the delbar-equation in a Banach space

Imre Patyi
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Abstract

We show that on the unit ball of a certain separable Banach space there is a smooth delbar-closed (0,1)-form which is not locally delbar-exact. Further, the Dolbeault isomorphism theorem does not generalize to arbitrary Banach spaces. Lastly, the Newlander-Nirenberg theorem does not generalize to arbitrary smooth integrable almost complex Banach manifolds.

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Imre Patyi. 1999-11-08. On the delbar-equation in a Banach space. https://arxiv.org/abs/math/9911045

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