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Real structure in unital separable simple C *-algebras with tracial rank zero and with a unique tracial state

2006
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New York Journal of Mathematics New York J. Math
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unpublished

Let A be a simple unital C *-algebra with tracial rank zero and with a unique tracial state and let Φ be an involutory *-antiautomorphism of A. It is shown that the associated real algebra A Φ = {a ∈ A : Φ(a) = a * } also has tracial rank zero. Let A be a unital simple separable C *-algebra with tracial rank zero and suppose that A has a unique tracial state. If Φ is an involutory *-antiautomorphism of A, then it is clear that the associated real algebra A Φ = {a ∈ A : Φ(a) = a * } is unital

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