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Positivstellensatzë for noncommutative rational expressions (1703.06951v1)
Published 20 Mar 2017 in math.FA and math.RA
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.