A Haagerup inequality through the use of orthogonal polynomials
Operator Algebras
2025-10-21 v1
Abstract
In this paper we prove that the Haagerup inequality for non-homogeneous polynomials in free semicircular variables of degree is optimal with a constant of order . 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 -Hermite polynomials.
Keywords
Cite
@article{arxiv.2510.16667,
title = {A Haagerup inequality through the use of orthogonal polynomials},
author = {Félix Parraud},
journal= {arXiv preprint arXiv:2510.16667},
year = {2025}
}