On the centralizer of rigid transformations
Sbornik. Mathematics, Tome 75 (1993) no. 2, pp. 445-472 Cet article a éte moissonné depuis la source Math-Net.Ru

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A rigid rank-2 transformation with trivial weak essential centralizer is constructed. A family of transformations with analogous properties but of infinite rank is also constructed.
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     author = {O. N. Ageev},
     title = {On the centralizer of rigid transformations},
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O. N. Ageev. On the centralizer of rigid transformations. Sbornik. Mathematics, Tome 75 (1993) no. 2, pp. 445-472. http://geodesic.mathdoc.fr/item/SM_1993_75_2_a7/

[1] Chacon R. V., Schwartzbaer T., “Commuting point transformations”, Z. Wahrscheinlichk. theorie and v. Geb., 11:4 (1969), 277–287 | DOI | MR | Zbl

[2] Ornstein D. S., “On the root problem in ergodic theory”, Proc. Sixth Berkeley Symp. Math. Stat. Prob., v. II, Univ. Calif. Press, 1967, 347–356 | MR

[3] Junco A., “A simple measure preserving transformation with trivial centralizer”, Pacif. J. Math., 79 (1978), 357–362 | MR

[4] King J. L., “The commutant is the weak closure of the powers for rank 1 transformations”, Erg. Th. and. Dyn. Sys., 6 (1986), 363–384 | MR | Zbl

[5] Friedman N., Gabriel P., King J., “An invariant for rigid rank 1 transformations”, Erg. Th. Dyn. Sys., 8 (1988), 53–72 | MR | Zbl

[6] Chacon R. V., “Transformations having continuous spectrum”, J. Math. and Mech., 16:5 (1966), 399–415 | MR | Zbl

[7] Junco A., “A transformation with simple spectrum which is not rank one”, Can. J. Math., 29 (1977), 655–663 | MR | Zbl

[8] Chacon R. V., “Approximation of transformations with continuous spectrum”, Pacif. J. Math., 31 (1969), 293–303 | MR

[9] Lemanczyk M., Sikorski A., “A class of not local rank one arising from continuous substitutions”, Prob. Theory and Rel. Fields, 76 (1987), 421–428 | DOI | MR | Zbl

[10] Kornfeld I. P., Sinai Ya. G., Fomin S. V., Ergodicheskaya teoriya, Nauka, M., 1980 | MR