Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-28T12:29:55.506Z Has data issue: false hasContentIssue false
  • English
  • Français

Théorème ergodique pour les opérateurs positifs à moyennes bornées sur les espaces Lp(1 < p < ∞)

Published online by Cambridge University Press:  19 September 2008

Antoine Brunel
Antoine Brunel
Affiliation:
Laboratoire de Probabilités, Université Pierre et Marie Curie, 4, Place Jussieu, Tour 56, 3ème Etage, 75252 Paris Cedex 05, France
Get access Rights & Permissions [Opens in a new window]

Abstract

The main result is a dominated ergodic theorem for a linear positive operator T on Lp(1 > p > ∞); the theorem holds if, and only if, T is Cesaro-bounded.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 2 , June 1992 , pp. 195 - 207
Copyright
Copyright © Cambridge University Press 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHIE

[1]Akcoglu, Mustafa A.. A pointwise ergodic theorem in Lp-spaces. Canad. J. Math. 27 (1975), 1075–1082.CrossRefGoogle Scholar
[2](Ionescu Tulcea) Bellow, Alexandra. Ergodic properties of isometries in Lp-spaces. Bull. Amer. Math. Soc. 70 (1964), 366–371.Google Scholar
[3]Derriennic, Yves & Lin, Michael. On invariant measures and ergodic theorems for positive operators. J Funct. Anal. 13 (1973) 252–267.CrossRefGoogle Scholar
[4]Emilion, Richard. Mean bounded operators and mean ergodic theorems. J. Funct. Anal. 61 (1985), 1–14.CrossRefGoogle Scholar
[5]Brunei, Antoine & Emilion, Richard. Sur les opérateurs positifs à moyennes bornées. C. R. Acad. Sci. Paris 298, sér 1, (6) (1984), 103–106.Google Scholar
[6]Burkholder, Donald L.. Maximal inequalities as necessary conditions for a.e. convergence. Z. Wahrsch. und Verw. Gebiete 3 (1964), 75–88.CrossRefGoogle Scholar
[7]Krengel, Ulrich. Ergodic theorems. de Gruyter Studies in Mathematics 6 (1985).Google Scholar
[8]Hewitt, Edwin and Stromberg, Karl. Real and Abstract Analysis. Springer, 1965.Google Scholar
[9]Brunel, Antoine. A pointwise ergodic theorem for positive, Cesaro-bounded operators on Lp(1 > p > ∞). Almost Everywhere Convergence. (Columbus, Ohio, 1988) Academic, Boston, 1989. pp. 153–158.Google Scholar