On the cohomology groups of holomorphic Banach bundles

Lempert, László

doi:10.1090/S0002-9947-09-04835-1

On the cohomology groups of holomorphic Banach bundles
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Trans. Amer. Math. Soc. 361 (2009), 4013-4025 Request permission

Abstract:

We consider a compact complex manifold $M$ and introduce the notion of two holomorphic Banach bundles $E,F$ over $M$ being compact perturbations of one another. Given two such bundles we show that if the cohomology groups $H^{q}(M,E)$ are finite dimensional, then so are the cohomology groups $H^{q}(M,F)$; as well as a more precise result in the same spirit.

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