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## Colloquium Mathematicum

2000 | 84/85 | 2 | 485-493
Tytuł artykułu

### On measure theoretical analogues of the Takesaki structure theorem for type III factors

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The orbit equivalence of type $III_{0}$ ergodic equivalence relations is considered. We show that it is equivalent to the outer conjugacy problem for the natural trace-scaling action of a countable dense ℝ-subgroup by automorphisms of the Radon-Nikodym skew product extensions of these relations. A similar result holds for the weak equivalence of arbitrary type $III_{0}$ cocycles with values in Abelian groups.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
485-493
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-09-22
poprawiono
2000-03-15
Twórcy
• Department of Mechanics and Mathematics, Kharkov National University, Freedom square 4, Kharkov, 61077, Ukraine
autor
• Graduate School of Mathematics, Kyushu University, Ropponmatsu Chuo-ku, Fukuoka, 810-8560, Japan
Bibliografia
• [BG] S. I. Bezuglyi and V. Ya. Golodets, Weak equivalence and the structure of cocycles of an ergodic automorphism, Publ. RIMS Kyoto Univ. 27 (1991), 577-635.
• [Da1] A. I. Danilenko, The topological structure of Polish groups and groupoids of measure space transformations, ibid. 31 (1995), 913-940.
• [Da2] A. I. Danilenko, Quasinormal subrelations of ergodic equivalence relations, Proc. Amer. Math. Soc. 126 (1998), 3361-3370.
• [FHM] J. Feldman, P. Hahn and C. C. Moore, Orbit structure and countable sections for actions of continuous groups, Adv. Math. 28 (1978), 186-230.
• [FM] J. Feldman and C. C. Moore, Ergodic equivalence relations, cohomology, and von Neumann algebras I, Trans. Amer. Math. Soc. 234 (1977), 289-324.
• [Go] V. Ya. Golodets, Description of representations of anticommutation relations, Uspekhi Mat. Nauk 24 (1969), no. 4, 3-64 (in Russian); English transl. in Russian Math. Surveys 24 (1969).
• [GS] V. Ya. Golodets and S. D. Sinel'shchikov, Classification and structure of cocycles of amenable ergodic equivalence relations, J. Funct. Anal. 121 (1994), 455-485.
• [Kr] W. Krieger, On ergodic flows and isomorphism of factors, Math. Ann. 223 (1976), 19-70.
• [Mo] C. C. Moore, Ergodic theory and von Neumann algebras, in: Proc. Symp. Pure Math. 38, Part 2, Amer. Math. Soc., 1982, 179-226.
• [Sc1] K. Schmidt, Cocycles of Ergodic Transformation Groups, Lecture Notes in Math. 1, MacMillan of India, Delhi, 1977.
• [Sc2] K. Schmidt, Algebraic Ideas in Ergodic Theory, CBMS Regional Conf. Ser. in Math. 76, Amer. Math. Soc., Providence, RI, 1990.
• [Ta] M. Takesaki, Duality for crossed product and the structure of von Neumann algebras of type III, Acta Math. 131 (1973), 249-310.
Typ dokumentu
Bibliografia
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