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arXiv · 2303.05790

The non-Archimedean Nirgendsnegativsemidefinitheitsstellensatz is not true

Hao Liang·Sizhuo Yan·Jianting Yang·Lihong Zhi
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Abstract

Klep and Schweighofer asked whether the Nirgendsnegativsemide-finitheitsstellensatz holds for a symmetric noncommutative polynomial whose evaluations at bounded self-adjoint operators on any nontrivial Hilbert space are not negative semidefinite. We provide an example to show the open problem has a negative answer.

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Hao Liang, Sizhuo Yan, Jianting Yang, Lihong Zhi. 2023-03-10. The non-Archimedean Nirgendsnegativsemidefinitheitsstellensatz is not true. https://arxiv.org/abs/2303.05790

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