# Characteristic Function of a Pure Commuting Contractive Tuple

Bhattacharyya, Tirthankar and Eschmeier, Joerg and Sarkar, Jaydeb (2005) Characteristic Function of a Pure Commuting Contractive Tuple. In: Integral Equations and Operator Theory, 53 (1). pp. 23-32.

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## Abstract

A theorem of Sz.-Nagy and Foias [9] shows that the characteristic function $\theta_T(z) = −T + zD_{T^*}(1_H - zT^*)^{-1}D_T$ 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 $C^n$. This function is related to the curvature invariant introduced by Arveson [3].

Item Type: Journal Article Copyright of this article belongs to Springer. Division of Physical & Mathematical Sciences > Mathematics 21 Jul 2008 19 Sep 2010 04:12 http://eprints.iisc.ernet.in/id/eprint/167