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On the Ergodic Hilbert Transform for Operators In Lp, 1 < p < ∞
Published online by Cambridge University Press: 20 November 2018
Abstract
In this paper the ergodic Hilbert transform is investigated at the operator theoretic level. Let T be an invertible positive operator on Lp = Lp(X, , μ) for some fixed p, 1 < p < ∞, such that sup{||Tn||p: — ∞ < n < ∞} < ∞. It is proved that the limit
exists almost everywhere and in the strong operator topology, where the prime denotes that the term with zero denominator is omitted. Related results are also proved.
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- Copyright © Canadian Mathematical Society 1987