Timeline for Completely contractive Banach algebra structure on the dual of a Hopf $C^*$-algebra
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Oct 19, 2023 at 15:52 | vote | accept | Andromeda | ||
| Oct 3, 2023 at 15:13 | comment | added | Andromeda | @MatthewDaws Thanks. I decided to give the bounty before it went away, but I still need to check some details. | |
| Oct 3, 2023 at 15:12 | history | bounty ended | Andromeda | ||
| Oct 3, 2023 at 14:52 | history | edited | Matthew Daws | CC BY-SA 4.0 |
Add correct hypthosis in point 1
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| Oct 3, 2023 at 14:49 | comment | added | Matthew Daws | Sorry, yes, I need a non-degeneracy condition. I'll edit the answer. | |
| Oct 2, 2023 at 17:24 | comment | added | Andromeda | Nevertheless, I still believe that $M(A\otimes A)\subseteq A^{**}\bar{\otimes}A^{**}$ is true, upon representating $A^{**}$ on a Hilbert space. Indeed, an element $z\in M(A\otimes A)$ is a strict limit of a bounded net in $A\odot A$, and on bounded subsets of $A\otimes A$, the strict topology agrees with the strong$^*$-topology, so the limit lives in $A^{**}\bar{\otimes}A^{**}$ as well. | |
| Oct 2, 2023 at 17:20 | comment | added | Andromeda | Thanks for the answer! I'm also a bit concerned about Step 1. If $M= B(H)$, I think we need to require that $A$ is a non-degenerate $*$-subalgebra of $M$ (see e.g. Lance's book), so an extra condition seems to be involved to make this work. | |
| Oct 2, 2023 at 16:57 | comment | added | Yemon Choi | Is there a reference for Step 1? I have a vague memory it might be in e.g. the book of Blecher and Le Merdy, but presumably there should be a more standard reference. | |
| Oct 2, 2023 at 15:42 | history | answered | Matthew Daws | CC BY-SA 4.0 |