## Unitary $N$-dilations for tuples of commuting matrices

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- by John E. McCarthy and Orr Moshe Shalit
- Proc. Amer. Math. Soc.
**141**(2013), 563-571 - DOI: https://doi.org/10.1090/S0002-9939-2012-11714-9
- Published electronically: June 11, 2012
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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 $q(T) = P_H q(U) |_H$ for all polynomials $q$ of degree at most $N$.## References

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## Bibliographic 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