Timeline for Examples of non-proper conditional expectations onto von Neumann subalgebras of $II_{1}$ factors
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| S Jul 18, 2017 at 4:04 | history | bounty ended | CommunityBot | ||
| S Jul 18, 2017 at 4:04 | history | notice removed | CommunityBot | ||
| Jul 12, 2017 at 3:06 | comment | added | Narutaka OZAWA | The result is a $\mathrm{II}_1$ analogue of a very well-known fact in matrix theory and seems to be rediscovered a few times. See for e.g., the recent paper of Dykema--Skoufranis for the reference. arxiv.org/abs/1503.05766 | |
| Jul 12, 2017 at 2:14 | comment | added | Jon Bannon | @NARUTAKA OZAWA: I was so happy to see what you wrote, I forgot to thank you for it! Thank you! | |
| Jul 12, 2017 at 1:46 | comment | added | Jon Bannon | @Narutaka OZAWA: I was hoping that this was the case! Do you happen to have a reference to Hiai's paper? If not, I will find it. | |
| Jul 12, 2017 at 1:41 | comment | added | Narutaka OZAWA | I think there is no such examples. By results of Hiai etc, a positive element $a$ in a $\mathrm{II}_1$ factor is in the norm- or weak*-closure of the convex hull of the unitary orbit of $x$ iff (the trace distribution function of) $a$ is majorized by $x$. That $E_N(x)$ is majorized by $x$ is proved in [Arveson and Kadison; Diagonals of self-adjoint operators] (it is stated there for masas $N$, but the proof works for general $N$). | |
| S Jul 10, 2017 at 2:06 | history | bounty started | Jon Bannon | ||
| S Jul 10, 2017 at 2:06 | history | notice added | Jon Bannon | Draw attention | |
| Jul 8, 2017 at 2:45 | history | edited | Jon Bannon | CC BY-SA 3.0 |
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| Jul 7, 2017 at 22:56 | history | edited | Jon Bannon | CC BY-SA 3.0 |
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| Jul 7, 2017 at 21:21 | history | asked | Jon Bannon | CC BY-SA 3.0 |