The Cuntz Semigroup, a Riesz Type Interpolation Property, Comparison and the Ideal Property
نویسندگان
چکیده
We define a Riesz type interpolation property for the Cuntz semigroup of a C∗-algebra and prove it is satisfied by the Cuntz semigroup of every C∗-algebra with the ideal property. Related to this, we obtain two characterizations of the ideal property in terms of the Cuntz semigroup of the C∗-algebra. Some additional characterizations are proved in the special case of the stable, purely infinite C∗-algebras, and two of them are expressed in language of the Cuntz semigroup. We introduce a notion of comparison of positive elements for every unital C∗-algebra that has (normalized) quasitraces. We prove that large classes of C∗-algebras (including large classes of AH algebras) with the ideal property have this comparison property. 2010 Mathematics Subject Classification: Primary: 46L35; Secondary: 46L05.
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