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ABELIAN FACES OF STATE-SPACES OF C-STAR-ALGEBRAS

Abstract:

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...

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Publication status:
Published

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Publisher copy:
10.1007/BF01962590

Authors


Publisher:
Springer-Verlag
Journal:
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume:
75
Issue:
1
Pages:
43-50
Publication date:
1980
DOI:
EISSN:
1432-0916
ISSN:
0010-3616
URN:
uuid:dafcb38a-35a8-4870-80c6-398fd5fa89d4
Source identifiers:
29001
Local pid:
pubs:29001
Language:
English

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