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Integral Equations and Operator Theory

, Volume 53, Issue 1, pp 23–32

# Characteristic Function of a Pure Commuting Contractive Tuple

Original Paper

## Abstract.

A theorem of Sz.-Nagy and Foias  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 .

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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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