Numerical ranges of $C_0(N)$ contractions
Functional Analysis
2010-12-03 v2 Complex Variables
Abstract
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.
Cite
@article{arxiv.1009.2249,
title = {Numerical ranges of $C_0(N)$ contractions},
author = {Chafiq Benhida and Pamela Gorkin and Dan Timotin},
journal= {arXiv preprint arXiv:1009.2249},
year = {2010}
}
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