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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Unitary $N$-dilations for tuples of commuting matrices
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by John E. McCarthy and Orr Moshe Shalit PDF
Proc. Amer. Math. Soc. 141 (2013), 563-571 Request permission

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 $q(T) = P_H q(U) |_H$ 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
  • MR Author ID: 271733
  • ORCID: 0000-0003-0036-7606
  • 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
  • MR Author ID: 829657
  • Email: oshalit@uwaterloo.ca, oshalit@math.bgu.ac.il
  • Received by editor(s): June 30, 2011
  • Published electronically: June 11, 2012
  • Communicated by: Marius Junge
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2996961