Blum–Hanson type ergodic theorems in noncommutative symmetric spaces

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

“…The proof relies on a 2x2-matrix argument combined with the result of [YeK79] which says that positive contractions acting on noncommutative L p -spaces have the Blum-Hanson property. Our theorem improves some results of [ChS17]. We refer to [AHR74], [Bel75], [FoS73], [LeM16], [LMP16] and [Net21] for related papers.…”