On the mean ergodic theorem of Sine
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- by Stuart P. Lloyd PDF
- Proc. Amer. Math. Soc. 56 (1976), 121-126 Request permission
Abstract:
Robert Sine has shown that $(1/n)(I + T + \cdots + {T^{n - 1}})$, the ergodic averages, converge in the strong operator topology iff the invariant vectors of $T$ separate the invariant vectors of the adjoint operator ${T^ \ast },T$ being any Banach space contraction. We prove a generalization in which (spectral radius of $T$) $\leqq 1$ replaces $||T|| \leqq 1$, and any bounded averaging sequence converging uniformly to invariance replaces the ergodic averages; it is necessary to assume that such sequences exist.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 56 (1976), 121-126
- MSC: Primary 47A35
- DOI: https://doi.org/10.1090/S0002-9939-1976-0451007-6
- MathSciNet review: 0451007