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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Ergodicity of the Cartesian product
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by Elias G. Flytzanis PDF
Trans. Amer. Math. Soc. 186 (1973), 171-176 Request permission

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
  • © Copyright 1973 American Mathematical Society
  • 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