Geodesic
Semi-Groups in L∞ And Local Ergodic Theorem
Canadian mathematical bulletin, Tome 29 (1986) no. 2, pp. 146-153

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DOI

We show that any W*-continuous semi-group in L∞ is L1 -norm continuous. As an application we prove the n-dimensional local ergodic theorem in L∞ . We also note that any bounded additive process in L∞ is absolutely continuous.For n = 1 this local theorem improves those of R. Sato [14] and D. Feyel [6] and for n ≥ 1 it generalizes M. Lin's ones which hold for positive operators [12].
DOI : 10.4153/CMB-1986-025-8
Mots-clés : 47A35, 47D05, 28A65 
Emilion, R. Semi-Groups in L∞ And Local Ergodic Theorem. Canadian mathematical bulletin, Tome 29 (1986) no. 2, pp. 146-153. doi: 10.4153/CMB-1986-025-8
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     title = {Semi-Groups in {L\ensuremath{\infty}} {And} {Local} {Ergodic} {Theorem}},
     journal = {Canadian mathematical bulletin},
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     year = {1986},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-025-8/}
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