4 papers
Noncommutative Rational Sums of Squares in Free Algebras
Sizhuo Yan, Jianting Yang, Lihong Zhi
This paper introduces rational sums of squares for symmetric noncommutative polynomials in free algebras. Under the assumption that the polynomial admits a strictly positive scalar…
A Homogeneous Nullstellensatz for Joint Invariant Subspaces
Sizhuo Yan, Jianting Yang, Lihong Zhi
Jurij Volčič conjectured that a noncommutative polynomial belongs to the unital -algebra generated by finitely many noncommutative polynomials if and only if, for m…
The non-Archimedean Nirgendsnegativsemidefinitheitsstellensatz is not true
Hao Liang, Sizhuo Yan, Jianting Yang +1
Klep and Schweighofer asked whether the Nirgendsnegativsemide-finitheitsstellensatz holds for a symmetric noncommutative polynomial whose evaluations at bounded self-adjoint operat…
A Characterization of Perfect Strategies for Mirror Games
Sizhuo Yan, Jianting Yang, Tianshi Yu +1
We associate mirror games with the universal game algebra and use the *-representation to describe quantum commuting operator strategies. We provide an algebraic characterization o…