PreprintCC BY 4.0arXiv
Talagrand type for noncommutative L1 spaces
Abstract
Let (ℳ,τ) be a semi-finite von Neumann algebra. We prove that L1(ℳ) has Talagrand type (1,ψ1,1), where ψ1,1(t)=t/log(e+t). As an consequence, the Schatten trace class S1 has Talagrand type (1,ψ1,1), 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.
Related
- Banach non-isomorphism of type III and semifinite noncommutative Lp-spaces
- On Talagrand Type
- ISOMETRIC EMBEDDING OF NONCOMMUTATIVE L_p -SPACES INTO NONCOMMUTATIVE SYMMETRIC SPACES
- Isometric embeddings of noncommutative Lp-spaces into noncommutative symmetric spaces
- Tingley's Problem for Haagerup Noncommutative Lp-Spaces, 1<p≠ 2<∞
BibTeX
@misc{luo2026talagrand,
title = {{Talagrand type for noncommutative $L_1$ spaces}},
author = {Sijie Luo and Yusen Wang and Dejian Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03407},
eprint = {2610.03407},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03407},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Talagrand type for noncommutative L_1 spaces
AU - Sijie Luo
AU - Yusen Wang
AU - Dejian Zhou
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03407
UR - https://arxiv.org/abs/2610.03407
AB - Let (ℳ,τ) be a semi-finite von Neumann algebra. We prove that L_1(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.
ER -