2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79360We 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. FranceComplex Variables58B12, 32C10, 32L20, 32F20, 46G20text