Journal article
POSITIVSTELLENSATZE FOR NONCOMMUTATIVE RATIONAL EXPRESSIONS
Proceedings of the American Mathematical Society, v 146(3), pp 933-937
01 Mar 2018
Abstract
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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Details
- Title
- POSITIVSTELLENSATZE FOR NONCOMMUTATIVE RATIONAL EXPRESSIONS
- Creators
- J. E. Pascoe - Washington University in St. Louis
- Publication Details
- Proceedings of the American Mathematical Society, v 146(3), pp 933-937
- Publisher
- Amer Mathematical Soc
- Number of pages
- 5
- Grant note
- DMS 1606260 / NSF Mathematical Science Postdoctoral Research Fellowship
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000423480000003
- Scopus ID
- 2-s2.0-85041513054
- Other Identifier
- 991021879624304721
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- Web of Science research areas
- Mathematics
- Mathematics, Applied