A noncommutative generalization of Hunter's positivity theorem

Published 16 Mar 2025 in math.FA and math.OA | (2503.12376v1)

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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