English

On the delbar-equation in a Banach space

Complex Variables 2007-05-23 v1

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.

Keywords

Cite

@article{arxiv.math/9911045,
  title  = {On the delbar-equation in a Banach space},
  author = {Imre Patyi},
  journal= {arXiv preprint arXiv:math/9911045},
  year   = {2007}
}

Comments

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

R2 v1 2026-07-22T18:05:06.367Z