Timeline for simple and non nuclear $C^*$-algebra
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 20, 2015 at 19:02 | comment | added | Yemon Choi | BTW I hope my comment wasn't perceived as denigrating the amenable iff nuclear results, which I hold in very high regard. It's just that sometimes they are used when there are easier, and more informative, approaches for particular examples one is considering | |
| Oct 20, 2015 at 18:59 | comment | added | Yemon Choi | @NikWeaver Who says I have to mention pink elephants? Oh, damn :) | |
| Oct 20, 2015 at 18:51 | comment | added | Nik Weaver | @YemonChoi: and yet you mentioned them ... | |
| Oct 20, 2015 at 15:59 | comment | added | Yemon Choi | Just because it is something I always go on about, I shall do so here :) ... Lance proved that $G$ is amenable iff ${\rm C}_r^*(G)$ is nuclear, using one of the original definitions of nuclearity. Then Bunce proved, without requiring any of Lance's results, that if ${\rm C}_r^*(G)$ is amenable as a Banach algebra and $G$ is discrete, then $\ell^\infty(G)$ has a (left or right or two-sided) invariant mean, so $G$ is amenable. I mention these in order to emphasize that non-nuclearity & non-amenability of ${\rm C}_r^*(F_2)$ can be discussed without mentioning the names of Connes or Haagerup :) | |
| Oct 20, 2015 at 15:50 | vote | accept | Albert harold | ||
| Oct 20, 2015 at 15:33 | comment | added | Ulrich Pennig | The only link I can find for Powers' paper is behind a paywall, sorry. | |
| Oct 20, 2015 at 15:33 | history | answered | Ulrich Pennig | CC BY-SA 3.0 |