Unitary N-dilations for tuples of commuting matrices

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 $N$.

arXiv comment11 pages