TY  - GEN
T1  - Characteristic function of a pure contractive tuple
A1  - Bhattacharyya,Tritha
A1  - Eschmeier,Jörg
A1  - Sarkar,Jaydeb
Y1  - 2012/02/15
N2  - A theorem of Sz.-Nagy and Foias [9] shows that the characteristic function \theta_{T}(z)=-T+zD_{T^{*}}(1_{\mathcal{\mathcal{H}}}-zT^{*})^{-1}D_{T} of a completly non-uniraty 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].
CY  - Saarbrücken
PB  - Universitäts- und Landesbibliothek
AD  - Postfach 151141, 66041 Saarbrücken
UR  - http://scidok.sulb.uni-saarland.de/volltexte/2012/4447
ER  -