Timeline for Extending maps from dense $*$-algebras of $C^*$-algebras
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jun 21, 2018 at 0:54 | comment | added | Ruy | Even though the answer is false in general, there are many special situations in which the extension does exist. This is discussed in Section 4 of [R. Exel, T. Giordano and D. Gonçalves, Enveloping algebras of partial actions as groupoid C*-algebras, J. Operator Theory, 65 (2011), 197-210]. | |
| Jun 20, 2018 at 18:38 | comment | added | Matthew Daws | Well, it was 5 years and 2 careers ago... I think this was just some private reading, and coming to the realisation that, well, this sort of question is subtle. Probably to do with getting from CQG algebras back to the $C^*$-algebra formalism; maybe Dijkhuizen's and Koornwinder's paper. | |
| Jun 20, 2018 at 17:24 | comment | added | Yemon Choi | Hi Matt, your comment rings a bell: was this one of your questions on here, or something we were discussing outside MO? | |
| Jun 20, 2018 at 15:59 | comment | added | Nik Weaver | It would be enough to know that the unitization of $\mathcal{A}$ is inverse closed ... | |
| Jun 20, 2018 at 15:58 | comment | added | Matthew Daws | Well, tautologically, yes! ($f$ by assumption extends to $A$...) Some years ago, I came across similar problems when working with Hopf $*$-algebras: it is rather subtle as to when you can extend such an $f$, and I don't recall having seen an "abstract" criteria: rather, there are domain specific arguments. So without knowing a lot more about $\mathcal A, \mathcal B$ and $f$ I doubt one can say more. Of course, I could be wrong... | |
| Jun 20, 2018 at 15:54 | comment | added | Max Schattman | Can one exclude such examples by asking more of $f$? | |
| Jun 20, 2018 at 15:54 | vote | accept | Max Schattman | ||
| Jun 20, 2018 at 15:49 | comment | added | Nik Weaver | That is lovely. | |
| Jun 20, 2018 at 15:48 | history | answered | Matthew Daws | CC BY-SA 4.0 |