English

A noncommutative generalization of Hunter's positivity theorem

Functional Analysis 2025-08-19 v2 Operator Algebras

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.

Keywords

Cite

@article{arxiv.2503.12376,
  title  = {A noncommutative generalization of Hunter's positivity theorem},
  author = {Stephan Ramon Garcia and Jurij Volčič},
  journal= {arXiv preprint arXiv:2503.12376},
  year   = {2025}
}

Comments

13 pages

R2 v1 2026-06-28T22:22:23.752Z