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Abstrakty
Let $ϕ_f$ be a Furstenberg transformation on the 2-torus $𝕋^2$ defined by $ϕ_{f}(x,y) = (e^{2πiθ}x, e^{2πif(x)}xy) for any x,y ∈ 𝕋, where θ is an irrational number and f is a real-valued continuous function on the 1-torus 𝕋. Let $A(ϕ_{f})$ be the crossed product associated with $ϕ_{f}$. We show that $A(ϕ_{f})$ has a unique tracial state for any irrational number θ and any real-valued continuous function f on 𝕋.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
183-187
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-11-30
Twórcy
autor
- Department of Mathematics, College of Science, Ryukyu University, Nishihara-Cho, Okinawa, 903-01 Japan
Bibliografia
- [1] H. Furstenberg, Strict ergodicity and transformation of the torus, Amer. J. Math. 83 (1961), 573-601.
- [2] K. Kodaka, Anzai and Furstenberg transformations on the 2-torus and topologically quasi-discrete spectrum, Canad. Math. Bull., to appear.
- [3] W. Parry, Topics in Ergodic Theory, Cambridge University Press, 1981.
- [4] G. K. Pedersen, C*-Algebras and their Automorphism Groups, Academic Press, 1979.
- [5] H. Rouhani, A Furstenberg transformation of the 2-torus without quasi-discrete spectrum, Canad. Math. Bull. 33 (1990), 316-322.
- [6] M. Takesaki, Theory of Operator Algebras I, Springer-Verlag, 1979.
- [7] J. Tomiyama, Invitation to C*-Algebras and Topological Dynamics, World Sci., Singapore, 1987.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv115i2p183bwm