25/11/2011, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
Chafiq Benhida, Laboratoire Paul Painlevé, Université de Lille 1, France
Numerical ranges of 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 contractions one can restrict the intersection to a smaller family of dilations. This generalizes a finite dimensional result of Gau and Wu.