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Unitary $ N$-dilations for tuples of commuting matrices


Authors: John E. McCarthy and Orr Moshe Shalit
Journal: Proc. Amer. Math. Soc. 141 (2013), 563-571
MSC (2010): Primary 47A20; Secondary 15A45, 47A57
DOI: https://doi.org/10.1090/S0002-9939-2012-11714-9
Published electronically: June 11, 2012
MathSciNet review: 2996961
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Abstract: We show that whenever a contractive $ k$-tuple $ T$ on a finite dimensional space $ H$ has a unitary dilation, then for any fixed degree $ N$ there is a unitary $ k$-tuple $ U$ on a finite dimensional space so that $ q(T) = P_H q(U) \vert _H$ for all polynomials $ q$ of degree at most $ N$.


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Additional Information

John E. McCarthy
Affiliation: Department of Mathematics, Washington University, St. Louis, Missouri 63130
Email: mccarthy@wustl.edu

Orr Moshe Shalit
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, ON N2L–3G1, Canada
Address at time of publication: Department of Mathematics, Ben-Gurion University of the Negev, Be’er-Sheva 84105, Israel
Email: oshalit@uwaterloo.ca, oshalit@math.bgu.ac.il

DOI: https://doi.org/10.1090/S0002-9939-2012-11714-9
Received by editor(s): June 30, 2011
Published electronically: June 11, 2012
Communicated by: Marius Junge
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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