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Integral Equations and Operator Theory

, Volume 53, Issue 1, pp 23–32 | Cite as

Characteristic Function of a Pure Commuting Contractive Tuple

  • T. BhattacharyyaEmail author
  • J. Eschmeier
  • J. Sarkar
Original Paper

Abstract.

A theorem of Sz.-Nagy and Foias [9] shows that the characteristic function \(\theta _T (z) = - T + zD_{T^*} (1_\mathcal{H} - zT^*)^{ - 1} D_T \) of a completely non-unitary contraction T is a complete unitary invariant for T. In this note we extend this theorem to the case of a pure commuting contractive tuple using a natural generalization of the characteristic function to an operator-valued analytic function defined on the open unit ball of \(\mathbb{C}^n .\) This function is related to the curvature invariant introduced by Arveson [3].

No Mathematics Subject Classification (2000).

No Keywords.

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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  2. 2.Fachbereich MathematikUniversität des SaarlandesSaarbrückenGermany

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