Timeline for 'Test Functions' to Lower Bound the Norm of Elements of Dual Quantum Group
Current License: CC BY-SA 3.0
21 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
|
|
| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
|
|
| S Jun 29, 2015 at 12:06 | history | bounty ended | JP McCarthy | ||
| S Jun 29, 2015 at 12:06 | history | notice removed | JP McCarthy | ||
| Jun 29, 2015 at 12:06 | vote | accept | JP McCarthy | ||
| Jun 29, 2015 at 11:55 | comment | added | Yemon Choi | OK, I've cobbled something together. Apologies for any earlier confusion | |
| Jun 29, 2015 at 11:54 | answer | added | Yemon Choi | timeline score: 1 | |
| Jun 29, 2015 at 6:44 | comment | added | JP McCarthy | Yemon... if you would care to submit a short collation of your comments as an answer I would like to give you the 50 rep. | |
| Jun 28, 2015 at 22:02 | comment | added | Yemon Choi | Correction to my earlier comment: while this result is in Dixmier's book, the "Section V.2" actually refers to Volume 1 of Takesaki's Theory of Operator Algebras | |
| Jun 28, 2015 at 21:59 | comment | added | Yemon Choi | It's the given, usual norm on $M$, and you want the formula I wrote, not the formula you wrote. The formula you wrote doesn't look right even in the simple case of $M=L^\infty[0,1]$ and $\tau(f)=\int_0^1 f(t)dt$ | |
| Jun 28, 2015 at 16:55 | comment | added | JP McCarthy | I am looking at Theorem 2.4.16 in Murphy and am wondering is that what you are thinking of... I am trying to clear up the issuee at math.stackexchange.com/questions/1342359/… | |
| Jun 28, 2015 at 16:46 | comment | added | JP McCarthy | @YemonChoi ... what norm is on $M$? Can this be done with the 1-norm: $\|x\|_1:=\tau(|x|)=\sup_{y\,:\,\tau(|y|)\leq1}|\tau(xy)|$. | |
| Jun 27, 2015 at 17:34 | comment | added | JP McCarthy | I will have a look. Thank you very much. When I find it I might ask you to put this as an answer so I can give you the 50 rep. | |
| Jun 27, 2015 at 17:15 | comment | added | Yemon Choi | It's in Dixmier's book on von Neumann algebras. I don't have a copy to hand but I once had to cite this fact and if I got it right, then it is in Section V.2 of his book (French version, but presumably also the English translation). I suspect it might originally be due to I. Segal back in the 1950s? | |
| Jun 27, 2015 at 16:58 | comment | added | JP McCarthy | Well cf. my first paragraph... have you got a reference or proof of this? | |
| Jun 27, 2015 at 14:11 | comment | added | Yemon Choi | Hmm, well perhaps I have misunderstood your question, but if $\tau$ is a faithful normal trace on a von Neumann algebra $M$, then IIRC $\tau((x^*x)^{1/2})$ is equal to the supremum of $|\tau(xy)|$ as $y$ runs over all elements in unit ball of M | |
| Jun 27, 2015 at 14:01 | comment | added | JP McCarthy | Yes to expressing it as a supremum --- or even greater than a supremum. You can assume Kac (and if this isn't enough tracial also). | |
| Jun 27, 2015 at 13:58 | comment | added | Yemon Choi | I find your question somewhat unclear. Are you merely asking for a way to express the noncommutative L^1-norm given by a tracial state as a supremum using the natural pairing? (Your definition of the 1-norm seems to be the usual one if the Haar state is tracial, as it is for Kac examples, but I am not sure it is the correct definition in the non-tracial case) | |
| S Jun 27, 2015 at 13:44 | history | bounty started | JP McCarthy | ||
| S Jun 27, 2015 at 13:44 | history | notice added | JP McCarthy | Draw attention | |
| Jun 24, 2015 at 17:09 | history | asked | JP McCarthy | CC BY-SA 3.0 |