Timeline for The functoriality of group C* algebra structure
Current License: CC BY-SA 2.5
10 events
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| Jun 18, 2010 at 20:06 | comment | added | skripka | Matt, Yemon, thank you very much, I've got it now. As far as reduced C* -algebra: is it functorial only for proper homomorphisms or condition of injectivity is sufficient? Thanks a lot. | |
| Jun 18, 2010 at 19:11 | comment | added | Matthew Daws | @Yemon: Yes, and, ahem, yes! | |
| Jun 18, 2010 at 19:11 | comment | added | Matthew Daws |
Yeah, okay, I was being vague. If $\ell^1(G)\rightarrow C^*(H)$ is injective then you're done: pull-back the norm from $C^*(H)$. Otherwise, you can only pull-back a seminorm, but this doesn't matter, as it's still dominated by the $C^*(G)$ norm.
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| Jun 18, 2010 at 19:07 | comment | added | Yemon Choi | Matt, I think some of your "norms" should perhaps be "seminorms"? Also, "Godement". | |
| Jun 18, 2010 at 18:13 | vote | accept | skripka | ||
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| Jun 18, 2010 at 18:13 | vote | accept | skripka | ||
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| Jun 18, 2010 at 18:13 | vote | accept | skripka | ||
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| Jun 18, 2010 at 18:13 | vote | accept | skripka | ||
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| Jun 18, 2010 at 18:06 | comment | added | skripka | Matt, thank you very much for your response! Your explanation of Q1 is great, I hope I understand all things maybe except one: could you explain how our * - homo l^1 (G)-> C*(H) defines a C*-norm on l^1(G)? As far as Q2, thank you, it is a good advice and we can provide a counterexample with a classical non - amenable group (free group of 2 generators) and free abelian group with 2 generators. Thank you very much one more time! | |
| Jun 18, 2010 at 15:48 | history | answered | Matthew Daws | CC BY-SA 2.5 |