On the cohomology groups of holomorphic Banach bundles

Abstract

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