Ergodicity of the Cartesian product
Author:
Elias G. Flytzanis
Journal:
Trans. Amer. Math. Soc. 186 (1973), 171-176
MSC:
Primary 28A65
DOI:
https://doi.org/10.1090/S0002-9947-1973-0328021-6
MathSciNet review:
0328021
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Abstract | References | Similar Articles | Additional Information
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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Additional Information
Keywords:
Ergodic transformation,
cartesian product,
eigenoperation,
Hilbert space,
unitary operator
Article copyright:
© Copyright 1973
American Mathematical Society