Speaker:
Ken Davidson, Pure Mathematics Department, University of Waterloo
A 3 × 3 matrix counterexample in dilation theory abstract:
We will discuss von Neumann’s inequality and unitary dilations of commuting n-tuples of matrix contractions. The success of dilations for a single operator, and then pairs of commuting operators, were followed by counterexamples for commuting triples. Counterexamples exist for 4 × 4 matrices. We provide an example of four commuting 3 × 3 matrices which do not dilate.