Timeline for $C(X)$ as finitely generated $C^*$-algebra
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 13, 2016 at 18:20 | vote | accept | mikis | ||
| Mar 13, 2016 at 16:48 | history | edited | Petr Naryshkin | CC BY-SA 3.0 |
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| Mar 13, 2016 at 16:34 | comment | added | Petr Naryshkin | Wait! In that case $C(X)$ will not be a Banach algebra at all! | |
| Mar 13, 2016 at 16:27 | comment | added | Petr Naryshkin | @NikWeaver But is that all such sets? What if $X$ is not locally compact? | |
| Mar 13, 2016 at 15:58 | comment | added | Nik Weaver | (It is usual to acknowledge comments when editing a post.) | |
| Mar 13, 2016 at 15:58 | comment | added | Nik Weaver | In response to the edit, compact subset of $\mathbb{R}^n$ if $C(X)$, closed subset of $\mathbb{R}^n$ if $C_0(X)$. | |
| Mar 13, 2016 at 14:25 | history | edited | Petr Naryshkin | CC BY-SA 3.0 |
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| Mar 13, 2016 at 14:23 | comment | added | Nik Weaver | To tighten this up, assuming $X$ is locally compact the condition is that it should be homeomorphic to a closed subset of $\mathbb{R}^n$ for some $n$. Its spectrum including $0$ is homeomorphic to a compact subset of $\mathbb{C}^n$, and after removing $0$ it has the form I stated. | |
| Mar 13, 2016 at 13:28 | history | answered | Petr Naryshkin | CC BY-SA 3.0 |