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Complex Analysis and Operator Theory

, Volume 12, Issue 7, pp 1729–1737 | Cite as

Completely Contractive Extensions of Hilbert Modules Over Tensor Algebras

  • Andrew K. Greene
Article
  • 16 Downloads

Abstract

This paper studies completely contractive extensions of Hilbert modules over tensor algebras over \(C^*\)-correspondences. Using a result of Sz-Nagy and Foiaş on triangular contractions, extensions are parametrized in terms of contractive intertwining maps between certain defect spaces. These maps have a simple description when initial data consists of partial isometries. Sufficient conditions for the vanishing and nonvanishing of completely contractive Hilbert module \({\text {Ext}}^1\) are given that parallel results for the classical disc algebra.

Keywords

Hilbert modules Extensions Derivations Tensor algebras 

Mathematics Subject Classification

Primary 46H25 Secondary 47L75 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsManhattan CollegeRiverdaleUSA
  2. 2.Quantitative Research, J.P. MorganNew YorkUSA

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