Geodesic
On the Ergodic Hilbert Transform for Operators In Lp, 1 < p < ∞
Canadian mathematical bulletin, Tome 30 (1987) no. 2, pp. 210-214

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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.
DOI : 10.4153/CMB-1987-030-3
Mots-clés : 47A35 
Sato, Ryotaro. On the Ergodic Hilbert Transform for Operators In Lp, 1 < p < ∞. Canadian mathematical bulletin, Tome 30 (1987) no. 2, pp. 210-214. doi: 10.4153/CMB-1987-030-3
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     author = {Sato, Ryotaro},
     title = {On the {Ergodic} {Hilbert} {Transform} for {Operators} {In} {Lp,} 1 &lt; p &lt; \ensuremath{\infty}},
     journal = {Canadian mathematical bulletin},
     pages = {210--214},
     year = {1987},
     volume = {30},
     number = {2},
     doi = {10.4153/CMB-1987-030-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-030-3/}
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