VANISHING COHOMOLOGY FOR HOLOMORPHIC VECTOR BUNDLES IN A BANACH SETTING

Abstract

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 H^q(Ω, E) vanish for q ≥ 1. We also give an application concerning neighborhoods of complex submanifolds.