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POSITIVSTELLENSATZE FOR NONCOMMUTATIVE RATIONAL EXPRESSIONS
Journal article   Open access   Peer reviewed

POSITIVSTELLENSATZE FOR NONCOMMUTATIVE RATIONAL EXPRESSIONS

J. E. Pascoe
Proceedings of the American Mathematical Society, v 146(3), pp 933-937
01 Mar 2018
url
https://doi.org/10.1090/proc/13773View
Published, Version of Record (VoR) Open

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
We derive some Positivstellensatze for noncommutative rational expressions from the Positivstellensatze 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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Web of Science research areas
Mathematics
Mathematics, Applied
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