A note on the Blum-Hanson property of some contractions on $\mathrm{L}^p$-spaces

Abstract

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.