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arXiv · 1703.06951

Positivstellensatzë for noncommutative rational expressions

J. E. Pascoe
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Abstract

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.

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J. E. Pascoe. 2017-03-20. Positivstellensatzë for noncommutative rational expressions. https://arxiv.org/abs/1703.06951

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