Geodesic
An Extrapolation Theorem for Contractions with Fixed Points
Canadian mathematical bulletin, Tome 24 (1981) no. 2, pp. 199-203

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In [9] de la Torre proved that if is a finite measure space and T is a linear operator on a real for some fixed p, 1 < p < ∞ , such that ||T||P ≤ 1 and simultaneously ||T||∞ ≤ l, and also such that there exists with Th = h and h≠0 a.e., then the dominated ergodic theorem holds for T, i.e. for every we have de la Torre proved his result, by showing that the operator S, defined by Sf = (sgn h) - T(f • sgn h) for is positive, and by applying Akcoglu's theorem [1] to S. 
Sato, Ryotaro. An Extrapolation Theorem for Contractions with Fixed Points. Canadian mathematical bulletin, Tome 24 (1981) no. 2, pp. 199-203. doi: 10.4153/CMB-1981-031-8
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     author = {Sato, Ryotaro},
     title = {An {Extrapolation} {Theorem} for {Contractions} with {Fixed} {Points}},
     journal = {Canadian mathematical bulletin},
     pages = {199--203},
     year = {1981},
     volume = {24},
     number = {2},
     doi = {10.4153/CMB-1981-031-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-031-8/}
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