Numerical ranges of $C_0(N)$ contractions

Details Numerical ranges of $C_0(N)$ contractions Numerical ranges of $C_0(N)$ contractions

2010-09-12

arxiv.org/abs/1009.2249v2

Mathematics

Functional Analysis

v1: 13 pages; v2: 14 pages; typos removed, title changed, slight change to the proof of Theorem 4.6. The final publication wil

Scientific paper

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.

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