Timeline for On strong convergence versus weak in operator topology and semi-continuity of the spectrum
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 6, 2021 at 8:17 | comment | added | András Bátkai | For selfadjoint operators, there are prositive results. See for example in Section 9.3 in Weidmann: Linear Operators in Hilbert space book for strong convergence.Theorem 9.19 states a detailed convergence result. | |
| Feb 6, 2021 at 8:10 | comment | added | András Bátkai | @MartinVäth this has been dicussed here many times before, see for example mathoverflow.net/a/231222/12898 or mathoverflow.net/q/262510/12898 | |
| Feb 5, 2021 at 19:54 | comment | added | Bazin | Yes, I was aware of that general result of semi-continuity but uniform convergence is way too much for me. I guess for instance that semi-continuity is not true under weak convergence, but I am not quite sure of what could happen for strong convergence. | |
| Feb 5, 2021 at 19:53 | answer | added | Martin Väth | timeline score: 2 | |
| Feb 5, 2021 at 19:48 | comment | added | Martin Väth | @András Bátkai, the spectrum is upper semicontinuous with respect to the operator norm. | |
| Feb 5, 2021 at 18:57 | comment | added | András Bátkai | There is huge literature on the fact the the spectrum is in general not continuous with respect to the operator norm. Which result do you mean in your first bullet point? | |
| Feb 5, 2021 at 17:57 | history | asked | Bazin | CC BY-SA 4.0 |