A 3×3 dilation counterexample
A 3×3 dilation counterexample
We define four 3×3 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 3×3 commuting contractions which are scalar plus nilpotent of order 2 do dilate to …