Please use this identifier to cite or link to this item: doi:10.22028/D291-26300
Title: Characteristic function of a pure contractive tuple
Author(s): Bhattacharyya, Tritha
Eschmeier, Jörg
Sarkar, Jaydeb
Language: English
Year of Publication: 2003
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: 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].
Link to this record: urn:nbn:de:bsz:291-scidok-44479
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 101
Date of registration: 15-Feb-2012
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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