| Data: |
2013 |
| Resum: |
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. |
| Drets: |
Tots els drets reservats.  |
| Llengua: |
Anglès |
| Document: |
Article ; recerca ; Versió publicada |
| Matèria: |
C* -algebra ;
The Cuntz semigroup ;
A Riesz type interpolation property ;
Ideal property ;
Comparison of positive elements ;
AH algebra |
| Publicat a: |
Publicacions matemàtiques, Vol. 57, Núm. 2 (2013) , p. 359-377, ISSN 2014-4350 |
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