  If $\Omega$ is a measure space, we show that absolute contractions which are
selfadjoint on $\mathrm{L}^2(\Omega)$ induce contractions on
$\mathrm{L}^p(\Omega)$ which satisfy the Blum-Hanson property. Our very short
argument relies on the use of noncommutative $\mathrm{L}^p$-spaces.
