Tracial states on crossed products associated with Furstenberg transformations on the 2-torus

• Autorzy: Kazunori Kodaka
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46L40: Automorphisms
• 46L30: States

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995
• Tom: 115
• Numer: 2
• Strony: 183-187

Daty

wydano

1995

otrzymano

1994-11-30

Twórcy

autor

Kazunori Kodaka

• 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.