Timeline for Show convergence of net associated to GNS-triplet associated to state on a $C^*$-algebra
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 12, 2021 at 13:52 | vote | accept | Andromeda | ||
| May 12, 2021 at 9:12 | comment | added | Andromeda | Ah, I guess that we have $u_\lambda \to u$ strongly in $A$ by non-degeneracy of the inclusion $A \subseteq B(H)$. But this is also in the strong topology on $B$ and then since the strong topology on $B$ is stronger than the weak$^*$-topology on bounded subsets, we find what you claim. Would that be correct? | |
| May 12, 2021 at 9:07 | comment | added | Andromeda | Thanks. Can you clarify why $(u_\lambda)$ converges to the identity in the weak$^*$-topology? | |
| May 12, 2021 at 8:23 | history | answered | Mateusz Wasilewski | CC BY-SA 4.0 |