Timeline for Completely contractive Banach algebra structure on the dual of a Hopf $C^*$-algebra
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Oct 19, 2023 at 15:52 | vote | accept | Andromeda | ||
| S Oct 3, 2023 at 15:12 | history | bounty ended | Andromeda | ||
| S Oct 3, 2023 at 15:12 | history | notice removed | Andromeda | ||
| Oct 2, 2023 at 15:42 | answer | added | Matthew Daws | timeline score: 4 | |
| Oct 2, 2023 at 5:19 | comment | added | Andromeda | @YemonChoi Thanks for your suggestion. I also thought about this: roughly, the idea would be to extend the map $\Delta: A \to M(A\otimes A)$ to a comultiplication $A^{**}\to A^{**}\bar{\otimes}A^{**}$. This dualises then to a multiplication map on $(A^{**})_* = A^{*}$. However, in general, it is not clear to me that we can find this extension to the bidual. In many cases of interest, this seems true: namely, it is true for those Hopf $C^*$-algebras that arise from a locally compact quantum group. Indeed, in that case the comultiplication is implemented by a multiplicative unitary. | |
| Oct 2, 2023 at 2:26 | history | edited | Yemon Choi |
Adding the OA tag to bring this to the attention of specialists who may know how to deal with this question
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| Oct 2, 2023 at 2:25 | comment | added | Yemon Choi | I don't have a complete answer, but the way this works for Hopf von Neumann algebras is that the vN spatial tensor product of M with itself can be identified with the dual of $M_* \hat\otimes M_*$ where $\hat\otimes$ is the projective tensor product of operator spaces. I suspect that one could try to adapt, or build on, this result by passing from A to its bidual, but I have not tried to check the details yet. | |
| S Sep 26, 2023 at 11:29 | history | bounty started | Andromeda | ||
| S Sep 26, 2023 at 11:29 | history | notice added | Andromeda | Draw attention | |
| Sep 25, 2023 at 12:12 | history | edited | Andromeda | CC BY-SA 4.0 |
added 36 characters in body
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| Sep 22, 2023 at 22:24 | history | edited | Andromeda | CC BY-SA 4.0 |
added 11 characters in body
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| Sep 22, 2023 at 8:33 | history | asked | Andromeda | CC BY-SA 4.0 |