Asian Journal of Mathematics
Volume 8 (2004)
VANISHING COHOMOLOGY FOR HOLOMORPHIC VECTOR BUNDLES IN A BANACH SETTING
Pages: 65 – 86
For a large class of Banach spaces X we prove the following. If Ω ⊂ X is open and pseudoconvex, and E → Ω is a locally trivial holomorphic Banach bundle, then the sheaf cohomology groups Hq(Ω, E) vanish for q ≥ 1. We also give an application concerning neighborhoods of complex submanifolds.