Timeline for Colimits of short exact sequences of C*-algebras
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Nov 20, 2020 at 14:23 | comment | added | Ruy | Alex, you are correct on both of your claims. Indeed what makes life so much easier when dealing with $^*$-homomomorphisms on C*-algebras is that every such map is isometric when the kernel is modded out, so, as you say, must have a closed range. I figure Banach space people must be very envious of us for this! | |
| Nov 20, 2020 at 7:01 | vote | accept | AlexE | ||
| Nov 20, 2020 at 7:00 | comment | added | AlexE | Looks good, thanks! I think that we need to use that images of ${}^*$-homomorphisms between $C^*$-algebras are closed, otherwise you might not be able to find the element $b$ in the first step. Actually, that the map $i$ is injective is also not completely trivial: I had to use that each of the maps $i_n$ is isometric since they are injective. | |
| Nov 19, 2020 at 18:00 | history | edited | Ruy | CC BY-SA 4.0 |
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| Nov 19, 2020 at 17:55 | history | edited | Ruy | CC BY-SA 4.0 |
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| Nov 19, 2020 at 17:49 | history | answered | Ruy | CC BY-SA 4.0 |