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Positivity and the Existence of Unitary Dilations of Commuting Contractions

  • J. Robert Archer
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 171)

Abstract

The central result of this paper is a method of characterizing those commuting tuples of operators that have a unitary dilation, in terms of the existence of a positive map with certain properties. Although this positivity condition is not necessarily easy to check given a concrete example, it can be used to find practical tests in some circumstances. As an application, we extend a dilation theorem of Sz.-Nagy and Foiaş concerning regular dilations to a more general setting

Keywords

Hilbert Space Trigonometric Polynomial Linear Manifold Defect Operator Positive Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • J. Robert Archer
    • 1
  1. 1.Department of MathematicsUniversity of GlasgowGlasgowUK

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