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Notes on modular conjugations of von Neumann factors. (English) Zbl 0976.46043

The authors present some results about the characterization of modular conjugations of von Neumann algebras. It is shown that all hyperfinite factors of type \(\text{II}\), \(\text{III}_1\) and \(\text{III}_{\lambda}\) have algebraic conjugations which are not modular conjugations.

MSC:

46L10 General theory of von Neumann algebras
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References:

[1] Baumgärtel, H. and M. Wollenberg: Causal Nets of Operator Algebras. Berlin: Akademie- Verlag 1992. · Zbl 0749.46038
[2] Bratteli, 0. and D. W. Robinson: Operator Algebras and Quantum Statistical Mechanics, Vol. I. New York: Springer 1979. · Zbl 0421.46048
[3] [5] Connes, A.: Noncornmutative Geometry. New York: Academic Press 1994.
[4] [7] Giordano, T., Skandalis, G. and E. J. Woods: On the computation of invariants for ITPFI factors. J. Oper. Theory 15 (1986), 83 - 107. · Zbl 0596.46057
[5] Kadison, R. V. and J. R. Ringrose: Fundamentals of the Theory of Operator Algebras, Vol II. New York: Academic Press 1986. · Zbl 0601.46054
[6] [11] Sakai, S.: Automorphisms and tensor products of operator algebras. Amer. J. Math. 97 (1976), 889 - 896. · Zbl 0321.46052 · doi:10.2307/2373678
[7] [13] Stratila, S.: Modular Theory in Operator Algebras. Bucuresti: Editura Academiei, and Tunbridge Wells: Abacus Press 1981.
[8] Stratila, S. and L. Zsido: Lectures on von Neumann algebras. Tunbridge Wells: Abacus Press 1979.
[9] Takesaki, M.: The Theory of Operator Algebras. New York: Springer 1979. · Zbl 0436.46043
[10] Takesaki, M.: The structure of the automorphism group of an AFD factor. Progr. Math. 92(1990), 19-44. 32/1997. · Zbl 0778.46044
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