Geodesic
A Dominated Ergodic Theorem for Contractions with Fixed Points
Canadian mathematical bulletin, Tome 20 (1977) no. 1, pp. 89-91

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

Let be a finite measure space, and let T be a contraction in real Lp (X). (i.e. T is linear and ||T||≤1). It is said that the Dominated Ergodic Theorem holds for T, if there exists a constant cp such that, if M(T)f(x) = supn 1/n then ||M(T)f||p ≤ cp ||f||p for every f in Lp . 
Torre, A. De La. A Dominated Ergodic Theorem for Contractions with Fixed Points. Canadian mathematical bulletin, Tome 20 (1977) no. 1, pp. 89-91. doi: 10.4153/CMB-1977-014-5
@article{10_4153_CMB_1977_014_5,
     author = {Torre, A. De La},
     title = {A {Dominated} {Ergodic} {Theorem} for {Contractions} with {Fixed} {Points}},
     journal = {Canadian mathematical bulletin},
     pages = {89--91},
     year = {1977},
     volume = {20},
     number = {1},
     doi = {10.4153/CMB-1977-014-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-014-5/}
}
TY  - JOUR
AU  - Torre, A. De La
TI  - A Dominated Ergodic Theorem for Contractions with Fixed Points
JO  - Canadian mathematical bulletin
PY  - 1977
SP  - 89
EP  - 91
VL  - 20
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-014-5/
DO  - 10.4153/CMB-1977-014-5
ID  - 10_4153_CMB_1977_014_5
ER  - 
%0 Journal Article
%A Torre, A. De La
%T A Dominated Ergodic Theorem for Contractions with Fixed Points
%J Canadian mathematical bulletin
%D 1977
%P 89-91
%V 20
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-014-5/
%R 10.4153/CMB-1977-014-5
%F 10_4153_CMB_1977_014_5

[1] 1. Akcoglu, M. A., A pointwise ergodic theorem in Lp-spaces, Can. J. Math., 27 (1975), 1075-1082. Google Scholar

[2] 2. Burkholder, D. L., Semi Gaussian subspaces, Trans. Amer. Math. Soc. 104 (1962), 123-131. Google Scholar

[3] 3. Dundford, N. and Schwartz, J. T., Convergence almost everywhere of operator averages, J. Math. Mech. 5 (1956), 129-178. Google Scholar

[4] 4. Hopf, E., On the ergodic theorem for positive linear operators, J. Reine Angew, Math. 205 (1960), 101-106. Google Scholar

[5] 5. McGrath, S. A. J., An abelian ergodic theorem for semigroups in L space, Proc. Amer. Math. Soc. 54 (1976), 231-236. Google Scholar

Cité par Sources :