Abstract
One formulation of D. Voiculescu’s theorem on approximate unitary equivalence is that two unital representations π and ρ of a separable C*-algebra are approximately unitarily equivalent if and only if rank o π = rank o ρ. We study the analog when the ranges of π and ρ are contained in a von Neumann algebra R, the unitaries inducing the approximate equivalence must come from R, and “rank” is replaced with “R-rank” (defined as the Murray-von Neumann equivalence of the range projection).
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References
Voiculescu, D., A non-commutative Weyl-von Neumann theorem, Rev. Roum. Math. Pure et Appl., 1976, 21: 97–113.
Hadwin, D., Non-separable approximate equivalence, Trans. Amer. Math. Soc., 1981, 266: 203–231.
Kadison, R. V., Ringrose, J. R., Fundamentals of the theory of operator algebras, Vols. I-IV, New York: Harcourt, 1986.
Arveson, W. B., An invitation to C*-algebras, New York: Springer-Verlag, 1976.
Elliott, G. A., Evans, D. E., The structure of the irrational rotation C*-algebra, Ann. Math., 1993, 138: 477–501.
Hadwin, D., Free entropy and approximate equivalence in von Neumann algebras, Operator algebras and operator theory (Shanghai, 1997), in Contemp. Math., 228, Providence: Amer. Math. Soc., 1998, 111–131.
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Ding, H., Hadwin, D. Approximate equivalence in von Neumann algebras. Sci. China Ser. A-Math. 48, 239–247 (2005). https://doi.org/10.1360/04ys0186
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DOI: https://doi.org/10.1360/04ys0186