On the delbar-equation in a Banach space

Details On the delbar-equation in a Banach space On the delbar-equation in a Banach space

1999-11-08

arxiv.org/abs/math/9911045v1

Mathematics

Complex Variables

13 pages, AmS-TeX, to appear in Bull. Soc. Math. France

Scientific paper

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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