Timeline for Can the intersection of a unitary and an irreducibly represented injective $C^*$-algebra be $\{0\}$?
Current License: CC BY-SA 4.0
6 events
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| May 17, 2021 at 10:09 | comment | added | Masayoshi Kaneda | Yeah, you are right. We do not know a priori that the representation is covariant. I was confused because in my context, which I did not present here, an injective $C^*$-algebra $A$ (this is different from the $\mathcal{A}$ in my question) is ``fixed,'' and for my purpose it suffices to have at least one irreducible representation $\mathcal{A}$ (this is same as $\mathcal{A}$ in my question) of $A$ that answers my question positively. | |
| May 17, 2021 at 0:28 | comment | added | Narutaka OZAWA | @Masayoshi Kaneda: It is $A_1$ that serves as a counterexample. | |
| May 14, 2021 at 15:05 | comment | added | Masayoshi Kaneda | In Case 2, $A_1$ is ``irreducibly'' represented on $H\oplus H$, but $A$ is not. So how is this case related to my question? | |
| May 14, 2021 at 0:20 | history | edited | Narutaka OZAWA | CC BY-SA 4.0 |
added 109 characters in body
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| May 13, 2021 at 10:20 | vote | accept | Masayoshi Kaneda | ||
| May 13, 2021 at 7:21 | history | answered | Narutaka OZAWA | CC BY-SA 4.0 |