Unitary 𝑁-dilations for tuples of commuting matrices

McCarthy, John; Shalit, Orr

doi:10.1090/S0002-9939-2012-11714-9

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 $N$.

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