Timeline for Perturbation in C*-Algebra
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 11, 2011 at 0:10 | comment | added | Yemon Choi | George: I can't get hold of the JFA paper online. I will try and have another look at Archbold's paper, but my first impression is that the example there is similar to your construction | |
| Jan 10, 2011 at 23:05 | comment | added | George Lowther | It seems that there is quite a bit of research about on this problem. E.g., if the algebra has trivial center then $K\in\{\frac12,1,\frac12+\frac{1}{\sqrt{3}}\}\cup[\frac32,\infty]$. And lots more surprising results besides that. Eg, plms.oxfordjournals.org/content/88/1/225.abstract | |
| Jan 10, 2011 at 22:44 | comment | added | George Lowther | Yemon: Thanks for that! I'm wondering if the examples in the last two papers you mention are along the same lines as mine? I just searched for them now, but not free access. | |
| Jan 10, 2011 at 17:38 | comment | added | Yemon Choi | I'd encourage people to vote up George Lowther's answer, since unlike me he used thought rather than MathSciNet and actually gave an explicit, informative counter-example | |
| Jan 10, 2011 at 17:29 | vote | accept | Qingyun | ||
| Jan 10, 2011 at 17:29 | vote | accept | Qingyun | ||
| Jan 10, 2011 at 17:29 | |||||
| Jan 10, 2011 at 17:29 | comment | added | Qingyun | This is exactly what I was looking for. Thank you guys! | |
| Jan 10, 2011 at 2:35 | comment | added | George Lowther | ...and replacing $\Vert x\Vert$ by $\inf\Vert x-z\Vert$ for $z$ in the center does reduce it to the same thing, for all $\epsilon < 1$. So, they are in fact the same statement. | |
| Jan 10, 2011 at 2:32 | comment | added | George Lowther | @Yemon: The original question is a bit weaker than the boxed statement here, and is effectively asking whether, for each $\epsilon > 0$, there is a $K(\epsilon)$ such that the distance of any point from the center is bounded by $\epsilon\Vert x\Vert + K(\epsilon)\sup_{\Vert y\Vert\le 1}\Vert xy-yx\Vert$. Your boxed statement is asking whether $K(\epsilon)$ is bounded above as $\epsilon\to0$, which is rather stronger (but maybe you can reduce it to the same thing). | |
| Jan 10, 2011 at 1:04 | history | answered | Yemon Choi | CC BY-SA 2.5 |