A Haagerup inequality through the use of orthogonal polynomials
Abstract
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.
Fields of Study & Subjects
Mathematical functions and polynomials
Advanced Optimization Algorithms Research
Matrix Theory and Algorithms
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Publication date
- 28 August 2026
- Language
- EN