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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Ergodicity of the Cartesian product


Author: Elias G. Flytzanis
Journal: Trans. Amer. Math. Soc. 186 (1973), 171-176
MSC: Primary 28A65
MathSciNet review: 0328021
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Abstract: $ {h_1}$ is an ergodic conservative transformation on a $ \sigma $-finite measure space and $ {h_2}$ is an ergodic measure preserving transformation on a finite measure space. We study the point spectrum properties of $ {h_1} \times {h_2}$. In particular we show $ {h_1} \times {h_2}$ is ergodic if and only if $ {h_1} \times {h_2}$ have no eigenvalues in common other than the eigenvalue 1. The conditions on $ {h_1},{h_2}$ stated above are in a sense the most general for the validity of this result.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0328021-6
PII: S 0002-9947(1973)0328021-6
Keywords: Ergodic transformation, cartesian product, eigenoperation, Hilbert space, unitary operator
Article copyright: © Copyright 1973 American Mathematical Society