Timeline for Weak-* convergence in $L^\infty((0,T)\times\Omega)$ implies weak-* convergence in $L^\infty(\Omega)$ for a.e. $t \in (0,T)$?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 7, 2020 at 18:08 | vote | accept | M.L | ||
| Feb 7, 2020 at 17:42 | answer | added | Giorgio Metafune | timeline score: 3 | |
| Feb 7, 2020 at 17:39 | comment | added | Giorgio Metafune | Ok, I will do. I was not sure about the question. | |
| Feb 7, 2020 at 17:20 | comment | added | Nik Weaver | @GiorgioMetafune: I think it's worth posting this as an answer. | |
| Feb 7, 2020 at 15:02 | comment | added | Giorgio Metafune | If I understood correctly the question, this is not true. If $u_n(t,x)=\sin (2\pi n\, t)f(x)$ for a fixed $f \neq 0$, then $u_n \to 0$, $w^*$ in $(t,x)$ by Riemann Lebesgue, but for fixed $t\neq 0,1/2,1$ does not converge $w^*$ in $x$. Similarly, there is no way to find a sequence $n_j$ such that $\sin (n_j t)$ converges a.e. Positivity does not help: tafe $f$ positive and add 1 to the sinus. | |
| Feb 7, 2020 at 10:41 | history | asked | M.L | CC BY-SA 4.0 |