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A mean ergodic theorem for families of contractions in Hilbert space


Authors: J. R. Blum and J. I. Reich
Journal: Proc. Amer. Math. Soc. 61 (1976), 183-185
MSC: Primary 47A35
DOI: https://doi.org/10.1090/S0002-9939-1976-0473875-4
MathSciNet review: 0473875
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Abstract: Let $ G$ be an LCA group and $ h$ a Hilbert space, and let $ T(g)$ be a function on $ G$ into the contractions on $ H$. Let $ \{ {\sigma _n}\} $ be a sequence of probability measures on $ G$. Under suitable conditions on $ T(g)$ and the sequence $ \{ {\sigma _n}\} $ we prove the strong convergence of the sequence $ {T_n} = \smallint T(g){\sigma _n}(dg)$. In certain cases we identify the limiting operator.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0473875-4
Article copyright: © Copyright 1976 American Mathematical Society

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