Timeline for Detecting isolated eigenvalues from local spectral measures
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 2, 2020 at 10:37 | vote | accept | Maurizio Moreschi | ||
| Oct 30, 2020 at 20:57 | comment | added | Maurizio Moreschi | Thank you for updating your answer. I am not going to modify the question again, but if with k=2 it's contradictory, then it is clear that I have not manage to get to the right formulation of what I want to ask yet (I have namely concrete examples of the situation I have in mind, when k=2). | |
| Oct 30, 2020 at 18:59 | history | edited | Christian Remling | CC BY-SA 4.0 |
added 982 characters in body
|
| Oct 30, 2020 at 14:48 | comment | added | Christian Remling | @MaurizioMoreschi: Yes, no problem, thanks for clarifying. I was just trying to make a general comment (especially since this is a widespread and somewhat unfortunate phenomenon on MO). | |
| Oct 30, 2020 at 12:52 | comment | added | Maurizio Moreschi | You are perfectly right, sorry. I didn't realize at all that there were something wrong with the formulation until reading your answer. The current formulation is what I really meant. | |
| Oct 30, 2020 at 12:47 | history | edited | Christian Remling | CC BY-SA 4.0 |
added 106 characters in body
|
| Oct 30, 2020 at 12:46 | comment | added | Christian Remling | If I may make a general comment, please try to avoid this kind of moving target question, where you change it to a different question after the first version has been answered. | |
| Oct 30, 2020 at 12:44 | comment | added | Christian Remling | @MaurizioMoreschi: Now it's a different situation, of course. There's a huge difference between "for all $x\in H_0$" (the question you asked originally) and "there is an ONB of $H_0$ for which..." (the edited version). | |
| Oct 30, 2020 at 11:24 | comment | added | Maurizio Moreschi | The case $k=1$ is indeed not very interesting. I have worked it out and added to the question. The positiveness of local spectral measures at zero would indeed imply that $T=0$ in the case $k=1$. | |
| Oct 30, 2020 at 9:34 | comment | added | Maurizio Moreschi | For the case $k=1$, I don't have any interesting example, so it might be that it would follow that $T=0$. In any case, I am actually mostly interested in the case $k\ge 2$ (in the example in the previous comment one has $k=2$). | |
| Oct 30, 2020 at 8:15 | comment | added | Maurizio Moreschi | I have adapted the formulation of the question a little to eliminate the only potential problem I could see. As an example, you can take the l^2 adjacency operator of a (c,d)-biregular tree with $c\ne d$. | |
| Oct 30, 2020 at 7:50 | comment | added | Maurizio Moreschi | Mmm, that's something weird going on. This question is motivated by many explicit examples that come up from my research in which clearly $T\ne 0$ and $H\ne H_0$. | |
| Oct 29, 2020 at 23:38 | history | answered | Christian Remling | CC BY-SA 4.0 |