ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract LetF be a closed face of the weak* compact convex state space of a unitalC*-algebraA. The class ofF-abelian states, introduced earlier by the author, is studied further. It is shown (without any restriction onA orF) thatF is a Choquet simplex if and only if every state inF isF-abelian, and that it is sufficient for this that every pure state inF isF-abelian. As a corollary, it is deduced that an arbitraryC*-dynamical system (A, G, α) isG-abelian if and only if every ergodic state is weakly clustering. Nevertheless the set of allF-abelian (or evenG-abelian) states is not necessarily weak* compact.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01962590
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