Functional Analysis and Applications Seminar 

25/11/2011, 15:00 — 16:00 — Room P3.10, Mathematics Building
Chafiq Benhida, Laboratoire Paul Painlevé, Université de Lille 1, France

Numerical ranges of $C_0(N)$ contractions

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.