Numerical ranges of $C_0(N)$ contractions
Chafiq Benhida, Pamela B. Gorkin, Dan Timotin · arXiv (Cornell University) · 2010
A conjecture of Halmos proved by Choi and Li states that the closure of the numerical range of a contraction on a Hilbert space is the intersection of the closure of the numerical ranges of all its unitary dilations. We show that for $C_0(N)$ contractions one can restrict the intersection to a smaller family of dilations. This generalizes a finite dimensional result of Gau and Wu.