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arXiv · 2503.12376

A noncommutative generalization of Hunter's positivity theorem

Stephan Ramon Garcia·Jurij Volčič
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Abstract

Hunter proved that the complete homogeneous symmetric polynomials of even degree are positive definite. We prove a noncommutative generalization of this result, in which the scalar variables are replaced with hermitian operators. We provide a sharp lower bound and a sum of hermitian squares representation that are novel even in the scalar case.

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Stephan Ramon Garcia, Jurij Volčič. 2025-03-16. A noncommutative generalization of Hunter's positivity theorem. https://arxiv.org/abs/2503.12376

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