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

Voir la notice de l'article provenant de la source Cambridge University Press

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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[1] 1. Akcoglu, M.A. and A. del Junco, Differentiation of additive processes, Canad. J. Math. 33, (1981) pp. 749–768 . Google Scholar

[2] 2. Akcoglu, M.A. and Krengel, U., A differentiation theorem for additive processes. Math. Z. 163 (1978), pp. 199–210. Google Scholar

[3] 3. Akcoglu, M.A. and Krengel, U., A differentiation theorem in Lp. Math. Z. 169 (1979), pp. 31–40. Google Scholar

[4] 4. Emilion, R., Continuity at 0 of semi-groups in Lt and differentiation of additive processes, Ann. Inst. H. Poincaré. (to appear). Google Scholar

[5] 5. Emilion, R., Additive and superadditive local theorems, (to appear). Google Scholar

[6] 6. Feyel, D., Sur une classe remarquable de processus abeliens. Math. Z. (to appear). Google Scholar

[7] 7. Hille, E. and Phillips, R.S., Functional analysis and semi-groups, (A.M.S. colloquium publications, Providence, 1957). Google Scholar

[8] 8. Kipnis, C., Majoration des semi-groupe s de contractions de Lt et applications, Ann. Inst. Poincaré Sect. B (N.S.), 10 (1974), pp. 369–384. Google Scholar

[9] 9. Krengel, U., A necessary and sufficient condition for the validity of the local ergodic theorem, Lecture Notes in Math. n° 89, 170-177; (Springer, Berlin - Heidelberg - New York, 1969). Google Scholar

[10] 10. Krengel, U., A local ergodic theorem, Invent. Math. 6 (1969), pp. 329–333. Google Scholar

[11] 11. Lin, M., Semi-groups of Markov operators, Boll. Un. Mat. Ital., (4) 6 (1972), pp. 20–44. Google Scholar

[12] 12. Lin, M., On local ergodic convergence of semi-group s and additive processes. Israel J. Math. Vol. 42, (1982), pp. 300–308. Google Scholar

[13] 13. Sato, R., On local ergodic theorems for positive semi-groups, Studia Math., 63, (1978), pp. 45—55. Google Scholar

[14] 14. Sato, R., Two local ergodic theorems on L», J. Math. Soc. Japan, Vol. 32, n° 3, 1980, pp. 415–423. Google Scholar

[15] 15. Wiener, N., The ergodic theorem, Duke Math. J. 5 (1939), pp. 1–18. Google Scholar

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