A 3x3 dilation counterexample
Operator Algebras
2014-02-26 v1 Functional Analysis
Abstract
We define four 3x3 commuting contractions which do not dilate to commuting isometries. However they do satisfy the scalar von Neumann inequality. These matrices are all nilpotent of order 2. We also show that any three commuting contractions which are scalar plus nilpotent of order 2 do dilate to commuting isometries.
Cite
@article{arxiv.1203.0062,
title = {A 3x3 dilation counterexample},
author = {Man Duen Choi and Kenneth R. Davidson},
journal= {arXiv preprint arXiv:1203.0062},
year = {2014}
}
Comments
11 pages