Timeline for $\tau (p) = \tau (q)$ for all normalized traces does not imply $p \sim q$
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Feb 8, 2021 at 10:05 | comment | added | Mikael de la Salle | @DavidHandelman I do not know what the OP wanted, but your interpretation of the question is indeed imore nteresting. Thanks for the argument. | |
| Feb 8, 2021 at 6:32 | vote | accept | Peg Leg Jonathan | ||
| Feb 7, 2021 at 21:33 | comment | added | David Handelman | I suspect that the OP wanted a simple C*-algebra which has a (necessarily faithful) trace. This is actually quite easy. Take any simple dimension group $G$ with infinitesimals; as a specific example, $Q^2$ with positive cone given by $0 \cup \{(a,b)| a + b > 0\}$; this has unique trace up to scalar multiple $(a,b) \mapsto a+b$; take as distinguished order unit (1,1)). There exists an AF C*algebra whose ordered K$_0$ group is $G$, and (1/2,-1/2) can be represented as [p-q] in K_0 where $p$ and $q$ are projections, e.g., represented by (1/2,0) - (0,1/2). The trace vanishes on this element. | |
| Feb 7, 2021 at 21:19 | history | answered | Mikael de la Salle | CC BY-SA 4.0 |