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The Cuntz semigroup, a Riesz type interpolation property, comparison and the ideal property
Pasnicu, Cornel
Perera, Francesc

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 ; publishedVersion
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 0214-1493

DOI: 10.5565/PUBLMAT_57213_04

19 p, 366.9 KB

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