Timeline for Question about Dirac operator
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 11, 2022 at 9:00 | comment | added | Bernd Ammann | With the original $\leq$ and $\geq$ the statement is certanly false. Take as counterexample the disjoint union of countably many S^2 of different radius. It is also not really a question about Dirac operators, but about operators in general. Thus the question is not really well-posed. | |
| Apr 10, 2022 at 15:41 | comment | added | user473423 | How can c be the minimum of the $\lambda$ which satisfy $|\lambda|\le c$? | |
| Apr 10, 2022 at 15:31 | comment | added | Radeha Longa | These c's are the same one. And I was confused about if the minimum of $\lambda_i$s' is a constant, not a function. @Echo | |
| Apr 10, 2022 at 15:01 | comment | added | user473423 | There seem to be two different c's here. | |
| Apr 10, 2022 at 14:21 | comment | added | Radeha Longa | I'm sure that the inequality is $\geq$. And I guess we can take the $c=\min\{\lambda_i\}$ to make our claim hold. Does it right?@Echo | |
| Apr 10, 2022 at 14:05 | comment | added | user473423 | Oh sorry, I read the inequality the other way round. But see, only this way your claim is true, otherwise it is false. Or did you mean $\le$ in your claim? | |
| Apr 10, 2022 at 11:55 | comment | added | Radeha Longa | Excuse me, I checked your calculation and I think it should be $|\lambda_i|^2\leq c^2$ for $\sigma\in H_+$. @Echo | |
| Apr 10, 2022 at 11:08 | comment | added | user473423 | If $\sigma=\sum_i\mu_if_i$ with $Df_i=\lambda_if_i$, then $\parallel D\sigma\parallel^2=\sum_i|\mu_i|^2|\lambda_i|^2\ge\sum_ic^2|\mu_i|^2=c^2\parallel \sigma\parallel^2$ | |
| Apr 10, 2022 at 7:15 | comment | added | Radeha Longa | Could you please write down your idea with some details? I can't follow you. Thanks a lot.@Echo | |
| Apr 10, 2022 at 7:13 | comment | added | user473423 | Express $\sigma$ in an orthonormal basis consisting of eigenvectors. | |
| Apr 10, 2022 at 4:10 | history | asked | Radeha Longa | CC BY-SA 4.0 |