Testing von Neumann inequalities with nilpotent matrices
Functional Analysis
2025-11-20 v3 Complex Variables
Abstract
We give an elementary proof of the folklore result that the Agler norm of a function is determined by its norm on commuting tuples of nilpotent matrices. The proof is variation on a standard cone separation argument. The topic is closely related to the Eschmeier-Patton-Putinar formulation of Carath\'eodory-Fej\'er interpolation.
Cite
@article{arxiv.2501.15671,
title = {Testing von Neumann inequalities with nilpotent matrices},
author = {Greg Knese},
journal= {arXiv preprint arXiv:2501.15671},
year = {2025}
}
Comments
Added some context to the main theorem, included an example and additional reference. Incorporated referee suggestions