A note on the Blum-Hanson theorem
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- by Lee Jones and Velimir Kuftinec PDF
- Proc. Amer. Math. Soc. 30 (1971), 202-203 Request permission
Abstract:
Let T be a linear contraction on an arbitrary Hilbert space. We prove that the weak convergence of the sequence $\{ {T^n}x\}$ implies the strong convergence of the averages of the sequences $\{ {T^{{k_i}}}x\}$ for all strictly increasing sequences $\{ {k_i}\}$ of positive integers.References
- J. R. Blum and D. L. Hanson, On the mean ergodic theorem for subsequences, Bull. Amer. Math. Soc. 66 (1960), 308–311. MR 118803, DOI 10.1090/S0002-9904-1960-10481-8
- Lee Kenneth Jones, A mean ergodic theorem for weakly mixing operators, Advances in Math. 7 (1971), 211–216 (1971). MR 285690, DOI 10.1016/S0001-8708(71)80001-4
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 202-203
- MSC: Primary 47.10; Secondary 28.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0281023-4
- MathSciNet review: 0281023