Abstract
What does the Cuntz semigroup really look like? We will see later that the question is out of reach in any reasonable sense without imposing some conditions on your C*-algebra. For this section, we restrict our attention to unital simple separable C*-algebras which have strict comparison of positive elements. In light of Example 2.0.5, we will also assume that our algebra is stably finite, since the Cuntz semigroup is otherwise degenerate. This means that our algebra admits at least one normalized 2-quasitrace (which will be a trace if the algebra is exact). The material covered in this section can be found in Brown–Perera–Toms [4] and Brown–Toms [5].
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Giordano, T., Kerr, D., Phillips, N.C., Toms, A. (2018). Structure of the Cuntz Semigroup. In: Perera, F. (eds) Crossed Products of C*-Algebras, Topological Dynamics, and Classification. Advanced Courses in Mathematics - CRM Barcelona. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-70869-0_3
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DOI: https://doi.org/10.1007/978-3-319-70869-0_3
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