Geodesic
Connections between the approximative and spectral properties of metric automorphisms
Matematičeskie zametki, Tome 13 (1973) no. 3, pp. 403-409 
A. M. Stepin. Connections between the approximative and spectral properties of metric automorphisms. Matematičeskie zametki, Tome 13 (1973) no. 3, pp. 403-409. http://geodesic.mathdoc.fr/item/MZM_1973_13_3_a8/
@article{MZM_1973_13_3_a8,
     author = {A. M. Stepin},
     title = {Connections between the approximative and spectral properties of metric automorphisms},
     journal = {Matemati\v{c}eskie zametki},
     pages = {403--409},
     year = {1973},
     volume = {13},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_3_a8/}
}
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To each automorphism $T$ of a Lebesgue space $(X,\mu) there corresponds a~unitary operator $U_T$ in the space $L^2(X,\mu)$, defined by the formula $(U_Tf)(x)=f(Tx)$, $f\in L^2(X,\mu)$, $x\in X$. In this note we investigate the special properties of the operator $U_T$ 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]).