Almost Uniform Convergence in Noncommutative Dunford-Schwartz Ergodic Theorem for $p>1$

Abstract

We prove that the ergodic Ces\' aro averages generated by a positive Dunford-Schwartz operator in a noncommutative space $L^p(\mathcal M,\tau)$, $1<p<\infty$, converge almost uniformly (in Egorov's sense). This problem goes back to the original paper of Yeadon \cite{ye}, where bilaterally almost uniform convergence of these averages was established for $p=1$.