Timeline for Commuting nets for commuting projections
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 2, 2014 at 5:52 | vote | accept | Mark Roelands | ||
| Sep 20, 2014 at 15:02 | comment | added | Mike Jury | @YemonChoi - Yes, that's a nice simplification and I think it still works; continuity at infinity would still force the $x_i(\infty)$ to be scalar multiples of $I_2$ which would prevent convergence. Also, I'm not sure why I wanted $q=1-p$ orginally; it seems like $q=p$ works fine. | |
| Sep 20, 2014 at 14:53 | comment | added | Yemon Choi | OK, I misunderstood earlier. This looks like it works - nice! Do you think we could run the same argument on $A=M_2 \otimes C({\bf N}\cup\{\infty\})$, sticking your all-entries-the-same projection at the point at infinity? | |
| Sep 20, 2014 at 3:03 | comment | added | Mike Jury | I'm not claiming that every element of the bidual looks like this, only that IF I have a bounded Borel function, I get an element of $C[0,1]^{**}$ out of it via $\langle f,\mu\rangle =\int f\, d\mu$. (And I guess I also need that for this part of the bidual, weak-$*$ convergence controls pointwise convergence, which is supposed to follow by testing against point masses.) | |
| Sep 20, 2014 at 2:54 | comment | added | Mike Jury | Not $L^\infty$, Borel; I am thinking $A^*$ is given by $M_2$-valued Radon measures $\mu$, and an $M_2$-valued Borel function $f$ acts on these by $\langle f, \mu \rangle= tr(\int f\, d\mu)$. (Am I all wet? This is why the bidual makes me nervous.) | |
| Sep 20, 2014 at 2:50 | comment | added | Yemon Choi | I agree you can map $A^{**}$ to $L^\infty([0,1], M_2)$ but I don't see how you are going back the other way | |
| Sep 20, 2014 at 2:40 | history | answered | Mike Jury | CC BY-SA 3.0 |