Almost uniform convergence in noncommutative Dunford-Schwartz ergodic theorem

Abstract

This article gives an affirmative solution to the problem whether the ergodic Cesáro averages generated by a positive Dunford-Schwartz operator in a noncommutative space $L^p(\mathcal{M},\ddot{I}„)$, $1\le p<\infty$, converge almost uniformly (in Egorov's sense). This problem goes back to the original paper of Yeadon, published in 1977, where bilaterally almost uniform convergence of these averages was established for $p=1$.

There is a critical flaw in the argument