Work

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

Year: 2026

Type: preprint

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}.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.31560

Authors: Ghorui, Hiranmoy, Mondal, Suman, Ray, Samya Kumar

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Arthritis National Research Foundation

OpenAlex ID: W7223388180

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