Timeline for A question about automorphisms of $II_1$ factors
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 23, 2012 at 1:23 | comment | added | mohanravi | Owen, thanks for pointing out that point $||\cdot||_2$ convergence gives the convergence of the associated correspondences. I now see why Inn($\mathcal{M}$) is closed in Aut($\mathcal{M}$) in this topology for property T factors. | |
| Jun 23, 2012 at 0:27 | comment | added | Owen Sizemore | Hmm, it's been a while since I looked at that. It is certainly true that you can also do it with the $\|\cdot\|_2$ norm, since that is the appropriate norm for also considering the convergence of the bimodules associated to the automorphisms. | |
| Jun 22, 2012 at 21:47 | comment | added | mohanravi | I just looked at the MathScinet review of Connes' paper - He uses the topology of pointwise norm convergence for the predual. He shows that if am ICC group has property T then the group of inner automorphisms is closed in Aut($L\Gamma$) in this aforementioned topology. I'll look through his paper more carefully to see if the same thing also holds for the point $||\cdot||_2$ topology. | |
| Jun 22, 2012 at 21:17 | history | answered | Owen Sizemore | CC BY-SA 3.0 |