A finiteness theorem for holomorphic Banach bundles
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 6 (2007) no. 1, pp. 15-37.

Let E be a holomorphic Banach bundle over a compact complex manifold, which can be defined by a cocycle of holomorphic transition functions with values of the form id +K where K is compact. Assume that the characteristic fiber of E has the compact approximation property. Let n be the complex dimension of X and 0qn. Then: If VX is a holomorphic vector bundle (of finite rank) with H q (X,V)=0, then dimH q (X,VE)<. In particular, if dimH q (X,𝒪)=0, then dimH q (X,E)<.

Classification: 32F10, 32C37
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     title = {A finiteness theorem for holomorphic {Banach} bundles},
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Leiterer, Jürgen. A finiteness theorem for holomorphic Banach bundles. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 6 (2007) no. 1, pp. 15-37. http://archive.numdam.org/item/ASNSP_2007_5_6_1_15_0/

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