Abstract:Given a (real or complex, separable) Banach space, and a contraction T on X, we say that T has the Blum-Hanson property if whenever x, y ∈ X are such that Tnx tends weakly to y in X as n tends to infinity, the means{1 \over N}\sum\limits_{k = 1}^N {{T^{{n_k}}}x} tend to y in norm for every strictly increasing sequence (nk) k≥1 of integers. The space X itself has the Blum-Hanson property if every contraction on X has the Blum-Hanson property. We explain the ergodic-theoretic motivation for the Blum-Hanson prope… Show more
“…This property has its origin in the paper [BlH60]. We refer to the survey [Gri19] and to the nice memoir [Oos09] for more information. It was independently proved in [JoK71] and [AkS72] that a Hilbert space has this property.…”
If Ω is a measure space, we show that absolute contractions which are selfadjoint on L 2 (Ω) induce contractions on L p (Ω) which satisfy the Blum-Hanson property. Our very short argument relies on the use of noncommutative L p -spaces.
“…This property has its origin in the paper [BlH60]. We refer to the survey [Gri19] and to the nice memoir [Oos09] for more information. It was independently proved in [JoK71] and [AkS72] that a Hilbert space has this property.…”
If Ω is a measure space, we show that absolute contractions which are selfadjoint on L 2 (Ω) induce contractions on L p (Ω) which satisfy the Blum-Hanson property. Our very short argument relies on the use of noncommutative L p -spaces.
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