Positivstellensatz\"e for noncommutative rational expressions
Functional Analysis
2017-03-22 v1 Rings and Algebras
Abstract
We derive some Positivstellensatz\"e for noncommutative rational expressions from the Positivstellensatz\"e for noncommutative polynomials. Specifically, we show that if a noncommutative rational expression is positive on a polynomially convex set, then there is an algebraic certificate witnessing that fact. As in the case of noncommutative polynomials, our results are nicer when we additionally assume positivity on a convex set-- that is, we obtain a so-called "perfect Positivstellensatz" on convex sets.
Cite
@article{arxiv.1703.06951,
title = {Positivstellensatz\"e for noncommutative rational expressions},
author = {J. E. Pascoe},
journal= {arXiv preprint arXiv:1703.06951},
year = {2017}
}
Comments
6 pages