Abstract
AbstractIn 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 limitexists 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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