Timeline for Construct a non-unital nuclear $C^*$-algebra without tracial states such that its multiplier algebra is also traceless
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 14, 2022 at 0:56 | comment | added | math112358 | @Leonel Rober, what about the examples of tracelss A where M(A) has no tracial states | |
| Jan 12, 2022 at 18:40 | comment | added | Leonel Robert | Hmmm, what seems harder to come by is examples of traceless A where M(A) has tracial states. I can only think of a very convoluted example. | |
| Jan 11, 2022 at 16:47 | comment | added | Jamie Gabe | I think you should try to work this out on your own. What would happen if $K(H)\otimes A$ or its multiplier algebra had a tracial state? Or if $B$ is such a nuclear $C^\ast$-algebra, what would happen if $A\otimes B$ or its multiplier algebra had a tracial state? | |
| Jan 11, 2022 at 16:23 | comment | added | math112358 | @InfiniteLooper, would you mind showing me a concrete example? | |
| Jan 11, 2022 at 16:22 | comment | added | math112358 | @Jamie Gabe，you mean $K(H)\otimes A$? | |
| Jan 10, 2022 at 15:56 | history | edited | LSpice | CC BY-SA 4.0 |
Elaborate title; proofreading
|
| Jan 10, 2022 at 13:44 | comment | added | InfiniteLooper | You can try twisted tensors also like ergodic group actions on measured space for example. | |
| Jan 10, 2022 at 13:43 | comment | added | Jamie Gabe | Try to think about what happens if you take any such example and tensor it with a C*-algebra. | |
| Jan 10, 2022 at 13:06 | history | asked | math112358 | CC BY-SA 4.0 |