Two Consequences of Brunel's Theorem
Canadian mathematical bulletin, Tome 34 (1991) no. 1, pp. 105-108

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

In this note we observe two consequences of Brunei's recent theorem. If T1,..., Tn are majorized by positive power-bounded operators S1,..., Sn of Lp, 1 < p < ∞, for which the ergodic theorem holds, then a multiple sequence ergodic theorem holds for T1,....,Tn . Further, the individual convergence for each Tk can be taken along uniform sequences.
DOI : 10.4153/CMB-1991-016-6
Mots-clés : 47A35, 28D99
Olsen, James H. Two Consequences of Brunel's Theorem. Canadian mathematical bulletin, Tome 34 (1991) no. 1, pp. 105-108. doi: 10.4153/CMB-1991-016-6
@article{10_4153_CMB_1991_016_6,
     author = {Olsen, James H.},
     title = {Two {Consequences} of {Brunel's} {Theorem}},
     journal = {Canadian mathematical bulletin},
     pages = {105--108},
     year = {1991},
     volume = {34},
     number = {1},
     doi = {10.4153/CMB-1991-016-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-016-6/}
}
TY  - JOUR
AU  - Olsen, James H.
TI  - Two Consequences of Brunel's Theorem
JO  - Canadian mathematical bulletin
PY  - 1991
SP  - 105
EP  - 108
VL  - 34
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-016-6/
DO  - 10.4153/CMB-1991-016-6
ID  - 10_4153_CMB_1991_016_6
ER  - 
%0 Journal Article
%A Olsen, James H.
%T Two Consequences of Brunel's Theorem
%J Canadian mathematical bulletin
%D 1991
%P 105-108
%V 34
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-016-6/
%R 10.4153/CMB-1991-016-6
%F 10_4153_CMB_1991_016_6

[1] 1. Baxter, J. R. and Olsen, J. H., Weighted and subsequential ergodic theorems, Can. J. Math. 35, 145–166. Google Scholar

[2] 2. Bellow, A. and Losert, V., The weighted pointwise ergodic theorem along subsequences, TAMS 288, 307– 346. Google Scholar

[3] 3. Brunei, A., A pointwise ergodic theorem for positive, Cesaro bounded operators on L(1 &lt; p &lt; ∞), proceedings of the International Conference on Almost Everywhere Convergence in Probability and Ergodic Theory, Columbus, Ohio, June 11-14, 1988, ed. by Edgar, G. A. and Sucheston, L., Academic Press, 1989, 153–157. Google Scholar

[4] 4. Brunei, A. and Keane, M., Ergodic theorems for operator sequences, ZW 12, 231–240. Google Scholar

[5] 5. McGrath, S. A., Some ergodic theorems for commuting L contractions, Studia Math. 70, 165–172. Google Scholar

[6] 6. Frangos, N. E. and Louis Sucheston, On multiparameter ergodic and martingale theorems in infinite measure spaces, Probab. Th. Rel. Fields 71 (1986), 477–490. Google Scholar

[7] 7. Olsen, J. H., Akcoglu's ergodic theorem for uniform sequences, Can. J. Math. 32, 880–884. Google Scholar

[8] 8. Olsen, J. H., A multiple sequence ergodic theorem, Can. Math. Bull. 26, 493—497. Google Scholar

[9] 9. Olsen, J. H., Multi-parameter weighted ergodic theorems from their single parameter version, Proceedings of the International Conference on Almost Everywhere Convergence in Probability and Ergodic Theory, Columbus, Ohio, June 11-14, 1988, ed. by Edgar, G. A. and Sucheston, L., Academic Press, 1989, 297–303. Google Scholar

Cité par Sources :