A Haagerup inequality through the use of orthogonal polynomials
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911219951075328 |
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| author | Parraud, Félix |
| author_facet | Parraud, Félix |
| contents | In this paper we prove that the Haagerup inequality for non-homogeneous polynomials in free semicircular variables of degree $n$ is optimal with a constant of order $n^{3/2}$. We also show an operator valued Haagerup inequality which improves on existing results. Our main tool to do so are free Chebyshev polynomials also known as $0$-Hermite polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16667 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Haagerup inequality through the use of orthogonal polynomials Parraud, Félix Operator Algebras In this paper we prove that the Haagerup inequality for non-homogeneous polynomials in free semicircular variables of degree $n$ is optimal with a constant of order $n^{3/2}$. We also show an operator valued Haagerup inequality which improves on existing results. Our main tool to do so are free Chebyshev polynomials also known as $0$-Hermite polynomials. |
| title | A Haagerup inequality through the use of orthogonal polynomials |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2510.16667 |