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: is an ergodic conservative transformation on a
-finite measure space and
is an ergodic measure preserving transformation on a finite measure space. We study the point spectrum properties of
. In particular we show
is ergodic if and only if
have no eigenvalues in common other than the eigenvalue 1. The conditions on
stated above are in a sense the most general for the validity of this result.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1973-0328021-6
Keywords:
Ergodic transformation,
cartesian product,
eigenoperation,
Hilbert space,
unitary operator
Article copyright:
© Copyright 1973
American Mathematical Society