Timeline for Reference request for translating from Top to C*-alg
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
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| Dec 13, 2021 at 14:21 | comment | added | LSpice | 0'' has 'non-generate' in place of 'non-degenerate'. | |
| Jul 20, 2021 at 12:03 | comment | added | user160032 | Representations $\pi: C(X) \to B(H)$ versus self-adjoint spectral measures $\mathcal{B}_X \to B(H)$? | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jul 16, 2015 at 16:41 | history | edited | Johannes Hahn | CC BY-SA 3.0 |
Some minor additions
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| Mar 9, 2013 at 20:43 | comment | added | Martin Brandenburg | This point explicitly only refers to degree $0$. Thank you for this extension. | |
| Mar 9, 2013 at 19:58 | comment | added | ThiKu | In Point 14 the right hand side should not be algebraic K theory, but topological K theory of C^* algebras. (Which agrees with algebraic K theory only in degree 0.) | |
| Jul 30, 2012 at 9:31 | comment | added | Rasmus | @Martin: I wanted to add sub-$C^*$-algebras to the list, but couldn't because your post is not CW. | |
| Dec 8, 2011 at 21:23 | comment | added | Martin Brandenburg | Indeed. I also used in my article which I linked for 0'). | |
| Dec 8, 2011 at 18:24 | comment | added | Yemon Choi | Depending on how one defines Gelfand theory (maximal modular ideals etc etc) for non-unital algebras, isn't 8) used in the proof that these categories are contravariantly equivalent? I am probably misremembering, though | |
| Dec 8, 2011 at 17:46 | history | edited | Martin Brandenburg | CC BY-SA 3.0 |
added 338 characters in body; added 4 characters in body
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| Dec 8, 2011 at 17:39 | comment | added | Martin Brandenburg | @MTS: The correct maps between locally compact hausdorff spaces are here proper maps. These have closed image. I will add this to 0). | |
| Dec 8, 2011 at 17:21 | comment | added | MTS | I think it's worth pointing out that (4) becomes more subtle when the spaces are locally compact but not compact. In that case, a map $f: X \to Y$ induces an injection $C(Y) \to C(X)$ if and only if the range of $f$ is dense in $Y$. Of course if $X$ is compact then $f(X)$ is closed, so there's no difference for compact spaces. | |
| Dec 8, 2011 at 14:41 | history | edited | Martin Brandenburg | CC BY-SA 3.0 |
added 288 characters in body; added 17 characters in body; edited body
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| Dec 8, 2011 at 14:32 | comment | added | Martin Brandenburg | Oh yes! I've included it. | |
| Dec 8, 2011 at 14:32 | history | edited | Martin Brandenburg | CC BY-SA 3.0 |
added 86 characters in body
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| Dec 8, 2011 at 13:45 | comment | added | Alain Valette | @Martin: nice list! At some point your list will include $K^*(X)=K_*(C(X))$, which is not considered trivial by any standard (= the Serre-Swan theorem). (:-) | |
| Dec 8, 2011 at 12:20 | history | answered | Martin Brandenburg | CC BY-SA 3.0 |