Chafiq Benhida, Pamela Gorkin, Dan Timotin
Published 2010-09-12, updated 2010-12-02Version 2
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.
Comments: v1: 13 pages; v2: 14 pages; typos removed, title changed, slight change to the proof of Theorem 4.6. The final publication will be available in IEOT at http://www.springerlink.com
The numerical range of a contraction with finite defect numbers
The $C$-numerical range and Unitary dilations
Numerical Range and Compressions of the Shift
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