Abstract
To each automorphism T of a Lebesgue space (X, Μ@#@) there corresponds a unitary operator UT in the space L2(X,Μ), defined by the formula (UTf) (x) = f (Tx),f ∃ L2(X,Μ), x ∃ X. In this note we investigate the special properties of the operator UT as a function of the rate of approximation of the automorphism T by periodic transformations (for the definition of the rate of approximation of a metric automorphism see [1]).
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A. B. Katok and A. M. Stepin, “Approximations in ergodic theory,” Usp. Mat. Nauk,22, No. 5, 81–106 (1967).
V. A. Rokhlin, “Lectures on entropy theory for transformations with invariant measure,” Usp. Mat. Nauk,22, No. 5, 3–56 (1967).
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Translated from Matematicheskie Zametki, Vol. 13, No. 3, pp.403–409, March, 1973.
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Stepin, A.M. Connections between the approximative and spectral properties of metric automorphisms. Mathematical Notes of the Academy of Sciences of the USSR 13, 244–247 (1973). https://doi.org/10.1007/BF01155664
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DOI: https://doi.org/10.1007/BF01155664