An atomic theory of ergodic spaces
R. Caballero, A. de la Torre (1985)
Studia Mathematica
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R. Caballero, A. de la Torre (1985)
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E. Atencia, F. Martin-Reyes (1984)
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F. Martín-Reyes, P. Ortega Salvador (1988)
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Ryotaro Sato (1988)
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F. J. Martin-Reyes (1986)
Annales de l'I.H.P. Probabilités et statistiques
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Ryotaro Sato (1987)
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A. de la Torre, F. Martín-Reyes (1987)
Studia Mathematica
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E. Atencia, A. de la Torre (1982)
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Yves Derriennic (2000)
Colloquium Mathematicae
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For a Cesàro bounded operator in a Hilbert space or a reflexive Banach space the mean ergodic theorem does not hold in general. We give an additional geometrical assumption which is sufficient to imply the validity of that theorem. Our result yields the mean ergodic theorem for positive Cesàro bounded operators in (1 < p < ∞). We do not use the tauberian theorem of Hardy and Littlewood, which was the main tool of previous authors. Some new examples, interesting for summability...
Roger Jones (1999)
Studia Mathematica
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We establish an exponential estimate for the relationship between the ergodic maximal function and the maximal operator associated with convolution powers of a probability measure.