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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0281023-4
PII: S 0002-9939(1971)0281023-4
Keywords: Mixing measure-preserving transformation, linear contraction, weak convergence, strong convergence
Article copyright: © Copyright 1971 American Mathematical Society