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• W2963133055 startingPage "1604" @default.
• W2963133055 abstract "For a separable unital C ⁎ -algebra A and a separable McDuff II 1 -factor M , we show that the space H om w ( A , M ) of weak approximate unitary equivalence classes of unital ⁎-homomorphisms A → M may be considered as a closed, bounded, convex subset of a separable Banach space – a variation on N. Brown's convex structure H om ( N , R U ) . Many separable unital C ⁎ -algebras, including all (separable unital) nuclear C ⁎ -algebras, have the property that for any McDuff II 1 -factor M , H om w ( A , M ) is affinely homeomorphic to the trace space of A . In general H om w ( A , M ) and the trace space of A do not share the same data (several examples are provided). We characterize extreme points of H om w ( A , M ) in many cases, and we give two different conditions – one necessary and the other sufficient – for extremality in general. The universality of C ⁎ ( F ∞ ) is reflected in the fact that for any unital separable A , H om w ( A , M ) may be embedded as a face in H om w ( C ⁎ ( F ∞ ) , M ) . We also extend Brown's construction to apply more generally to H om ( A , M U ) ." @default.
• W2963133055 created "2019-07-30" @default.
• W2963133055 creator A5089849713 @default.
• W2963133055 date "2016-09-01" @default.
• W2963133055 modified "2023-09-24" @default.
• W2963133055 title "Convex sets associated to C⁎-algebras" @default.
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• W2963133055 doi "https://doi.org/10.1016/j.jfa.2016.05.020" @default.
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