PreprintCC BY 4.0arXiv
Failure of noncommutative Rota's theorem with Llog L endpoint
Abstract
We construct a factorizable Markov map T on a hyperfinite finite von Neumann algebra and a positive element x∈ Llog L for which the sequence Tn(T*)n x does not converge bilaterally almost uniformly. This answers a question of Anantharaman-Delaroche \cite{AD2006}.
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BibTeX
@misc{ghorui2026failure,
title = {{Failure of noncommutative Rota's theorem with $L\log L$ endpoint}},
author = {Hiranmoy Ghorui and Suman Mondal and Samya Kumar Ray},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31560},
eprint = {2610.31560},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31560},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Failure of noncommutative Rota's theorem with Llog L endpoint
AU - Hiranmoy Ghorui
AU - Suman Mondal
AU - Samya Kumar Ray
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31560
UR - https://arxiv.org/abs/2610.31560
AB - We construct a factorizable Markov map T on a hyperfinite finite von Neumann algebra and a positive element x∈ Llog L for which the sequence T^n(T^*)^n x does not converge bilaterally almost uniformly. This answers a question of Anantharaman-Delaroche \cite{AD2006}.
ER -