Unitary N-dilations for tuples of commuting matrices

Details Unitary N-dilations for tuples of commuting matrices Unitary N-dilations for tuples of commuting matrices

2011-05-10

arxiv.org/abs/1105.2020v1

Mathematics

Functional Analysis

11 pages

Scientific paper

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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