On the ergodic power function for invertible positive operators

Ryotaro Sato

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Ergodic power functions for mean bounded, invertible, positive operators

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On a ratio ergodic theorem

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On the mean ergodic theorem for Cesàro bounded operators

Yves Derriennic (2000)

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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 $L^{p}$ (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...