Geodesic
Weighted and Subsequential Ergodic Theorems
Canadian journal of mathematics, Tome 35 (1983) no. 1, pp. 145-166

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

1. Introduction. Let (X, , μ) be a probability space, T a linear operator on Lp (X, , μ), for some p, 1 ≦ p ≦ ∞. Let an be a sequence of complex numbers, n = 0, 1, ..., which we shall often refer to as weights. We shall say that the weighted pointwise ergodic theorem holds for T on Lp , if, for every ƒ in Lp , 1.1 Let a denote the sequence (an). If (1.1) holds we shall say that a is Birkhoff for T on Lp , or, more briefly, that (a, T) is Birkhoff.We are also interested in ergodic theorems for subsequences. Let n(k) be a subsequence. We shall say the pointwise ergodic theorem holds for the subsequence n(k) and the operator T if, for every ƒ in Lp , 1.2 
Baxter, J. R.; Olsen, J. H. Weighted and Subsequential Ergodic Theorems. Canadian journal of mathematics, Tome 35 (1983) no. 1, pp. 145-166. doi: 10.4153/CJM-1983-010-7
@article{10_4153_CJM_1983_010_7,
     author = {Baxter, J. R. and Olsen, J. H.},
     title = {Weighted and {Subsequential} {Ergodic} {Theorems}},
     journal = {Canadian journal of mathematics},
     pages = {145--166},
     year = {1983},
     volume = {35},
     number = {1},
     doi = {10.4153/CJM-1983-010-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-010-7/}
}
TY  - JOUR
AU  - Baxter, J. R.
AU  - Olsen, J. H.
TI  - Weighted and Subsequential Ergodic Theorems
JO  - Canadian journal of mathematics
PY  - 1983
SP  - 145
EP  - 166
VL  - 35
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-010-7/
DO  - 10.4153/CJM-1983-010-7
ID  - 10_4153_CJM_1983_010_7
ER  - 
%0 Journal Article
%A Baxter, J. R.
%A Olsen, J. H.
%T Weighted and Subsequential Ergodic Theorems
%J Canadian journal of mathematics
%D 1983
%P 145-166
%V 35
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-010-7/
%R 10.4153/CJM-1983-010-7
%F 10_4153_CJM_1983_010_7

[1] 1. Akcoglu, M. A., A pointwise ergodic theorem in L-spaces, Can. J. Math. 27 (1975), 1975–1982. Google Scholar

[2] 2. Akcoglu, M. A. and Sucheston, L., Dilations of positive contractions on L-spaces, Can. J. Math. Bull. 20 (1977), 285–292. Google Scholar

[3] 3. Bellow, A., Ergodic properties of isometries in L-spaces, 1 < p < °°, Bull. A.M.S. 70 (1964), 366–371. Google Scholar

[4] 4. Blum, J. R. and Cogburn, R., On ergodic sequences of measures, Proc. A.M.S. 51 (1975), 359–365. Google Scholar

[5] 5. Blum, J. R. and Reich, J. E., p-sets for random walks, Z. Wahrscheinlichkeitstheorie and Verw. Gebiete 48 (1979), 193–200. Google Scholar

[6] 6. Brunei, A. and Keane, M., Ergodic theorems for operator sequences, Z. Wahrscheinlichkeitstheorie and Verw. Gebiete 12 (1969), 231–240. Google Scholar

[7] 7. de la Torre, A., A simple proof of the maximal ergodic theorem, Can. J. Math. 28 (1976), 1073–1075. Google Scholar

[8] 8. Dunford, N. and Schwartz, J., Linear operators I (John Wiley, New York, 1958). Google Scholar

[9] 9. Kan, C., Ergodic properties of Lamperti operators, Can. J. Math. 80 (1978), 1206–1214. Google Scholar

[10] 10. Halmos, P. and Von Neumann, J., Operator methods in classical mechanics II, Annals of Math. 43 (1942), 333–350. Google Scholar

[11] 11. Olsen, J. H., Akcoglu's ergodic theorem for uniform sequences, Can. J. Math. 32 (1980), 880–884. Google Scholar

[12] 12. Olsen, J. H., The individual weighted ergodic theorem for bounded Besicovitch sequences, Can. Bull. Math. 25 (1982), 468–471. Google Scholar

[13] 13. Olsen, J. H., The individual ergodic theorem for Lamperti contractions, C. R. Math. Rep. Acad. Sci. Canada 3 (1981), 113–118. Google Scholar

[14] 14. Ornstein, D. S. and Shields, P. C., Mixing Markov shifts of kernel type are Bernoulli, Adv. Math. 10 (1973), 143–146. Google Scholar

[15] 15. Reich, J. I., On the individual ergodic theorem for subsequences, Annals of Prob. 5 (1977), 1039–1046. Google Scholar

[16] 16. Ryll-Nardzewski, C., Topics in ergodic theory, in Proceedings of the Winter School in Probability, Karpacz, Poland, 131-156, Lecture Notes in Mathematics 472 (Springer-Verlag, Berlin 1975). Google Scholar

[17] 17. Sato, R., Operator averages for subsequences, Math. J. of Okayama University 22 (1980). Google Scholar

Cité par Sources :