Timeline for C*-Algebras: Dynamics vs. Derivations
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Nov 18, 2014 at 16:50 | vote | accept | C-star-W-star | ||
| Nov 18, 2014 at 7:34 | answer | added | Michael | timeline score: 6 | |
| Nov 18, 2014 at 2:13 | comment | added | C-star-W-star | @NikWeaver: Denseness I checked but I'm still hanging at the point that showing that exponentiating really recovers the group at least on a dense domain. Then the rest would be just a result by uniform extension. | |
| Nov 18, 2014 at 2:08 | comment | added | C-star-W-star | Yep, I mean $t_n\to t$ implies $\tau^{t_n}(A)\to\tau^t(A)$ for every $A\in\mathcal{A}$. In principle that is nothing but continuity w.r.t. sort of pointwise topology. | |
| Nov 18, 2014 at 2:07 | comment | added | Nik Weaver | I guess the hint would be that exponentiating the generators should recover the one-parameter groups. The key technical point is that the generators have dense domain, which you can prove using a mollifier. | |
| Nov 18, 2014 at 1:56 | history | edited | C-star-W-star | CC BY-SA 3.0 |
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| Nov 18, 2014 at 1:53 | comment | added | C-star-W-star | @JonBannon; No, I mean infinitesimal generator but there's no Hilbert space and so neither a concept of selfadjointness nor unitarity. All I have is a C*-algebra and a strongly continuous one-parameter group of automorphisms and that's the problem as I pointed out. | |
| Nov 18, 2014 at 0:55 | history | edited | C-star-W-star | CC BY-SA 3.0 |
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| Nov 18, 2014 at 0:50 | history | asked | C-star-W-star | CC BY-SA 3.0 |