Similarity of Quotient Hilbert modules in the Cowen-Douglas Class

2012/12/12 by Kui Ji, Jaydeb Sarkar, Ji, Kui +1
Mathematics · #Holomorphic and Operator Theory #Geometry and complex manifolds #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1212.2707

Abstract

In this paper, we consider the similarity and quasi-affinity problems for Hilbert modules in the Cowen-Douglas class associated with the complex geometric objects, the hermitian anti-holomorphic vector bundles and curvatures. Given a "simple" rank one Cowen-Douglas Hilbert module M, we find necessary and sufficient conditions for a class of Cowen-Douglas Hilbert modules satisfying some positivity conditions to be similar to M ⊗ ℂ^m. We also show that under certain uniform bound condition on the anti-holomorphic frame, a Cowen-Douglas Hilbert module is quasi-affinity to a submodule of the free module M ⊗ ℂ^m.

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