Asian Journal of Mathematics

Volume 8 (2004)

Number 1

VANISHING COHOMOLOGY FOR HOLOMORPHIC VECTOR BUNDLES IN A BANACH SETTING

Pages: 65 – 86

DOI: http://dx.doi.org/10.4310/AJM.2004.v8.n1.a7

Author

LÁSZLÓ LEMPERT

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

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