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A note on the Blum-Hanson theorem

Lee Jones, Velimir Kuftinec

Source record

Source: Crossref

Published: Sep 1, 1971

DOI: 10.1090/s0002-9939-1971-0281023-4

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Source abstract

Let T be a linear contraction on an arbitrary Hilbert space. We prove that the weak convergence of the sequence { T n x } \{ {T^n}x\} implies the strong convergence of the averages of the sequences { T k i x } \{ {T^{{k_i}}}x\} for all strictly increasing sequences { k i } \{ {k_i}\} of positive integers.

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A note on the Blum-Hanson theorem — Mathematical Frontier Network