2017/03/20 by Pascoe, J. E.
#13J30 #15A22 #16K40 #26C15 #47A63 (Secondary) #47L07 (Primary) #FOS: Mathematics #Functional Analysis (math.FA) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1703.06951
We derive some Positivstellensatzë for noncommutative rational expressions from the Positivstellensatzë 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.