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<p>Klep and Schweighofer asked whether the Nirgendsnegativsemidefinitheitsstellensatz 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.</p>

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The non-Archimedean Nirgendsnegativsemidefinitheitsstellensatz is not true

  • 期刊论文

  • 发表日期：

    2025年2月3日

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  • Hao Liang,
  • Sizhuo Yan,
  • Jianting Yang,
  • Lihong Zhi

摘要

Klep and Schweighofer asked whether the Nirgendsnegativsemidefinitheitsstellensatz 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.