Timeline for G-abelian systems
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| May 26, 2020 at 19:50 | comment | added | francesco fidaleo | The relation is explained in one of the comments above. | |
| May 26, 2020 at 15:38 | comment | added | LSpice | What is the relation of the title to your question? I.e., would an example of the sort you want be called a G-abelian (or is it $G$-abelian?) system? | |
| May 26, 2020 at 10:35 | comment | added | francesco fidaleo | In commutative case, it does hold true: ${\rm dim}(E[H])=1\iff \phi$ is ergodic. Maybe, it is true also if the support of $\phi$ in the bidual is central. | |
| May 26, 2020 at 10:31 | history | edited | francesco fidaleo | CC BY-SA 4.0 |
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| May 26, 2020 at 9:45 | comment | added | francesco fidaleo | No Adrian, ergodicity means extremality among invariant states. ${\rm dim}(E[H])=1$ implies ergodicity, but the converse is true under the additional assumption of $G$-abelianess (in our situation $Z$-abelianess), see Prop. 3.1.12 in Sakai's book. The question is that, at my best knowledge, conterexamples don't exist in literature | |
| May 26, 2020 at 9:30 | comment | added | Adrián González Pérez | Doesn't the fact that $\dim(E[H]) \geq 2$ contradict the ergodicity of $\phi$? It does in the commutative case. | |
| May 25, 2020 at 11:40 | review | First posts | |||
| May 25, 2020 at 12:40 | |||||
| May 25, 2020 at 11:38 | history | edited | YCor |
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| May 25, 2020 at 11:36 | history | asked | francesco fidaleo | CC BY-SA 4.0 |