Two ergodic theorems for convex combinations of commuting isometries
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- by S. A. McGrath PDF
- Proc. Amer. Math. Soc. 40 (1973), 229-234 Request permission
Abstract:
Let $(X,\mathcal {F},\mu )$ be a measure space. In this paper we obtain ${L^p}$ estimates for the supremum of the CesΓ ro averages of combinations of commuting isometries of ${L^p}(X,\mathcal {F},\mu )$. In particular, we show that a convex combination of two invertible commuting isometries of ${L^p}(X,\mathcal {F},\mu ),p$ fixed, $1 < p < \infty ,p \ne 2$, admits of adominated estimate with constant $P/(p - 1)$. We also show that a convex combination of an arbitrary number of commuting positive invertible isometries of ${L^2}(X,\mathcal {F},\mu )$ admits of a dominated estimate with constant 2.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 229-234
- MSC: Primary 47A35; Secondary 28A65
- DOI: https://doi.org/10.1090/S0002-9939-1973-0318927-1
- MathSciNet review: 0318927