On the delbar-equation in a Banach space
Abstract
Description
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.
13 pages, AmS-TeX, to appear in Bull. Soc. Math. France
13 pages, AmS-TeX, to appear in Bull. Soc. Math. France