A noncommutative generalization of Hunter's positivity theorem
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908491280547840 |
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| author | Garcia, Stephan Ramon Volčič, Jurij |
| author_facet | Garcia, Stephan Ramon Volčič, Jurij |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12376 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A noncommutative generalization of Hunter's positivity theorem Garcia, Stephan Ramon Volčič, Jurij Functional Analysis Operator Algebras 05E05, 13J30, 15A45, 16S10 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. |
| title | A noncommutative generalization of Hunter's positivity theorem |
| topic | Functional Analysis Operator Algebras 05E05, 13J30, 15A45, 16S10 |
| url | https://arxiv.org/abs/2503.12376 |