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arXiv · 2610.03407

Talagrand type for noncommutative $L_1$ spaces

Sijie Luo·Yusen Wang·Dejian Zhou
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Abstract

Let $(\mathcal{M},τ)$ be a semi-finite von Neumann algebra. We prove that $L_1(\mathcal{M})$ has Talagrand type $(1,ψ_{1,1})$, where $ψ_{1,1}(t)=t/\log(e+t)$. As an consequence, the Schatten trace class $S_1$ has Talagrand type $(1,ψ_{1,1})$, thus settled an open problem of Question 2 in Cordero-Erausquin and Eskenazis (2023). Our proof is based on the noncommutative Mazur maps initiated by Ricard.

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Sijie Luo, Yusen Wang, Dejian Zhou. 2026-10-02. Talagrand type for noncommutative $L_1$ spaces. https://arxiv.org/abs/2610.03407

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