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Titlebook: Crossed Products of C*-Algebras, Topological Dynamics, and Classification; Thierry Giordano,David Kerr,Andrew Toms,Francesc P Textbook 201

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eans 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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P. Koundouri,M. Stithou,P. Melissourgosor a detailed treatment of this invariant. In the case of a unital .*-algebra, the invariant becomes ., where [1.] is the K.-class of the unit, and T(.) is the (compact convex) space of tracial states. We will concentrate on unital .*-algebras in the sequel in order to limit technicalities.
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P. Koundouri,M. Stithou,P. Melissourgos In this section we will introduce and discuss a conjectural version of such a principle, one that has significant evidence to support it. The conjecture relates three regularity properties for .*-algebras which we introduce presently.
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Novice Scientists and Expert Scientists results, such as stable rank one, real rank zero, order on traces determined by projections, strict comparison of positive elements, or .-stability. Some results with conclusions of this sort are stated in these notes, but mostly without proof.
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