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Unitary invariants for Hilbert modules of finite rank

  • Shibananda Biswas EMAIL logo , Gadadhar Misra and Mihai Putinar

Abstract

We associate a sheaf model to a class of Hilbert modules satisfying a natural finiteness condition. It is obtained as the dual to a linear system of Hermitian vector spaces (in the sense of Grothendieck). A refined notion of curvature is derived from this construction leading to a new unitary invariant for the Hilbert module. A division problem with bounds, originating in Douady's privilege, is related to this framework. A series of concrete computations illustrate the abstract concepts of the paper.

Received: 2010-06-07
Revised: 2010-09-10
Published Online: 2012-January
Published in Print: 2012-January

Walter de Gruyter Berlin New York 2012

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