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A note on the Blum-Hanson theorem

Authors: Lee Jones and Velimir Kuftinec
Journal: Proc. Amer. Math. Soc. 30 (1971), 202-203
MSC: Primary 47.10; Secondary 28.00
MathSciNet review: 0281023
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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 [Enhancements On Off] (What's this?)

  • [1] J. R. Blum and D. L. Hanson, On the mean ergodic theorem for subsequences, Bull. Amer. Math. Soc. 66 (1960), 308-311. MR 22 #9572. MR 0118803 (22:9572)
  • [2] L. K. Jones, A mean ergodic theorem for weakly mixing operators, Advances in Math. (to appear). MR 0285690 (44:2908)

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Keywords: Mixing measure-preserving transformation, linear contraction, weak convergence, strong convergence
Article copyright: © Copyright 1971 American Mathematical Society

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