2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142543In the present paper we consider a von Neumann algebra M with a faithful normal semi-finite trace $\t$, and $\{α_ t\} $ a strongly continuous extension to $L^p(M,\t)$ of a semigroup of absolute contractions on $L^1 (M,τ)$. By means of a non-commutative Banach Principle we prove for a Besicovitch function b and $x\in L^p(M,\t)$, the averages \frac{1}{T}\int_0^Tb(t)\a_t(x)dt converge bilateral almost uniform in $L^p(M,\t)$ as $T\to 0$.11 pages. submittedOperator AlgebrasFunctional Analysis46L50, 46L55, 46L53, 47A35, 35A99text