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arXiv · 2610.31560

Failure of noncommutative Rota's theorem with $L\log L$ endpoint

Hiranmoy Ghorui·Suman Mondal·Samya Kumar Ray
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Abstract

We construct a factorizable Markov map $T$ on a hyperfinite finite von Neumann algebra and a positive element $x\in L\log L$ for which the sequence $T^n(T^*)^n x$ does not converge bilaterally almost uniformly. This answers a question of Anantharaman-Delaroche \cite{AD2006}.

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Hiranmoy Ghorui, Suman Mondal, Samya Kumar Ray. 2026-10-22. Failure of noncommutative Rota's theorem with $L\log L$ endpoint. https://arxiv.org/abs/2610.31560

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