ABELIAN FACES OF STATE-SPACES OF C-STAR-ALGEBRAS
Let F be a closed face of the weak* compact convex state space of a unital C*-algebra A. The class of F-abelian states, introduced earlier by the author, is studied further. It is shown (without any restriction on A or F) that F is a Choquet simplex if and only if every state in F is F-abelian, and...
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| Format: | Journal article |
| Language: | English |
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Springer-Verlag
1980
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| Summary: | Let F be a closed face of the weak* compact convex state space of a unital C*-algebra A. The class of F-abelian states, introduced earlier by the author, is studied further. It is shown (without any restriction on A or F) that F is a Choquet simplex if and only if every state in F is F-abelian, and that it is sufficient for this that every pure state in F is F-abelian. As a corollary, it is deduced that an arbitrary C*-dynamical system (A, G, α) is G-abelian if and only if every ergodic state is weakly clustering. Nevertheless the set of all F-abelian (or even G-abelian) states is not necessarily weak* compact. © 1980 Springer-Verlag. |
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