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}
}
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13 pages