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    Brunel, Antoine 2002. Le théorème ergodique pour les opérateurs positifs sur les espaces Lp (1<p<∞) revisité. Comptes Rendus Mathematique, Vol. 334, Issue. 3, p. 205.


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

  • Antoine Brunel (a1)
  • DOI:
  • Published online: 01 September 2008

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.

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[1]Mustafa A. Akcoglu . A pointwise ergodic theorem in Lp-spaces. Canad. J. Math. 27 (1975), 10751082.

[3]Yves Derriennic & Michael Lin . On invariant measures and ergodic theorems for positive operators. J Funct. Anal. 13 (1973) 252267.

[4]Richard Emilion . Mean bounded operators and mean ergodic theorems. J. Funct. Anal. 61 (1985), 114.

[6]Donald L. Burkholder . Maximal inequalities as necessary conditions for a.e. convergence. Z. Wahrsch. und Verw. Gebiete 3 (1964), 7588.

[8]Edwin Hewitt and Karl Stromberg . Real and Abstract Analysis. Springer, 1965.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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