A NONCOMMUTATIVE GENERALIZATION OF HUNTER’S POSITIVITY THEOREM

Stephan Ramon Garcia; Jurij Volčič

doi:10.1090/proc/17480

A NONCOMMUTATIVE GENERALIZATION OF HUNTER’S POSITIVITY THEOREM

Stephan Ramon Garcia
, Jurij Volčič

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	585-597
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	154
Issue number	2
DOIs	https://doi.org/10.1090/proc/17480
State	Published - 1 Jan 2026
Externally published	Yes

Keywords

Hunter’s inequality
complete homogeneous symmetric polynomial
hermitian sum of squares
noncommutative polynomial

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/proc/17480

Cite this

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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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AB - 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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KW - complete homogeneous symmetric polynomial

KW - hermitian sum of squares

KW - noncommutative polynomial

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A NONCOMMUTATIVE GENERALIZATION OF HUNTER’S POSITIVITY THEOREM

Abstract

Keywords

ASJC Scopus subject areas

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