Timeline for A question about automorphisms of $II_1$ factors
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 11, 2023 at 8:25 | comment | added | Yanyu | Would you like to give me any reference for the equivalence about pointwse converges in 2-norm and pointwise convergence in $M_*$? | |
| Jul 4, 2012 at 21:33 | comment | added | Jesse Peterson | The equivalence between non-property $\Gamma$, and the subgroup of inner-automorphisms being closed is due independently to Sakai, "On automorphism groups of II$_1$-factors", 1974 (ams.org/mathscinet-getitem?mr=380443), and Connes, "Almost periodic states and factors of type III$_1$, 1974 (ams.org/mathscinet-getitem?mr=358374). See for instance the MathSciNet reviewers remarks on Sakai's paper. | |
| Jul 4, 2012 at 14:31 | history | edited | mohanravi | CC BY-SA 3.0 |
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| Jun 23, 2012 at 7:38 | comment | added | Jesse Peterson | Also, to which paper of Effros are you referring? | |
| Jun 23, 2012 at 7:37 | comment | added | Jesse Peterson | I think that perhaps you are confusing topologies. For II$_1$ factors it is much more common to study the topology of pointwise converges in the 2-norm. (Which is equivalent to pointwise convergence in $M_*$.) The characterization of property $\Gamma$ that I know uses this topology and not the topology of pointwise norm convergence in $M$. | |
| Jun 22, 2012 at 21:17 | answer | added | Owen Sizemore | timeline score: 1 | |
| Jun 22, 2012 at 17:45 | comment | added | mohanravi | Thinking about Owen Sizemore's comment, I just realised that it is not clear to me whether the point $||\cdot||_2$ limit of a net of automorphisms of a $II_1$ factor is an automorphism. It is an unital *endomorphism certainly, but why should it be onto? | |
| Jun 22, 2012 at 15:35 | comment | added | Owen Sizemore | Actually the point wise $\|\cdot\|_2$ topology is really the appropriate topology for studying Aut(M). Because in this topology you can use the Hilbert space structure. For example, Popa's notion of malleable deformation is a one-parameter family that converges to the identity in point wise $\|\cdot\|_2$ | |
| Jun 22, 2012 at 14:35 | history | asked | mohanravi | CC BY-SA 3.0 |