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

Hiranmoy Ghorui, Suman Mondal, Samya Kumar Ray

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 $T^n(T^{\ast }{)}^{n}x$ does not converge…