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

TL;DR

This paper demonstrates that certain selfadjoint absolute contractions on L^2 spaces induce contractions on L^p spaces with the Blum-Hanson property, using noncommutative L^p-space techniques.

Contribution

It provides a concise proof that selfadjoint absolute contractions on L^2 induce contractions with the Blum-Hanson property on L^p, leveraging noncommutative L^p-space methods.

Findings

Selfadjoint absolute contractions induce contractions with the Blum-Hanson property on L^p.

The proof uses noncommutative L^p-space techniques.

The result applies to measure spaces with specific contraction properties.

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.