A mean ergodic theorem for families of contractions in Hilbert space
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- by J. R. Blum and J. I. Reich PDF
- Proc. Amer. Math. Soc. 61 (1976), 183-185 Request permission
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.References
- Julius Blum and Bennett Eisenberg, Generalized summing sequences and the mean ergodic theorem, Proc. Amer. Math. Soc. 42 (1974), 423–429. MR 330412, DOI 10.1090/S0002-9939-1974-0330412-0
- Béla Sz.-Nagy and Ciprian Foiaş, Harmonic analysis of operators on Hilbert space, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York; Akadémiai Kiadó, Budapest, 1970. Translated from the French and revised. MR 0275190
Additional Information
- © Copyright 1976 American Mathematical Society
- 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