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Unitary N-dilations for tuples of commuting matrices
Published 10 May 2011 in math.FA, math.OA, and math.RA | (1105.2020v1)
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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