Timeline for What is Quantization ?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 3, 2014 at 0:50 | history | edited | Eric Peterson | CC BY-SA 3.0 |
fixed mathjax error
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| Nov 12, 2011 at 6:43 | comment | added | Theo Johnson-Freyd | But of course you're right, there's something wrong with the statement, because any indiscrete space has only the constant functions, which clearly form a commutative c-star algebra. Probably I should have added the word "Hausdorff" somewhere --- there's no chance of recovering non-Hausdorff structure from continuous $\mathbb C$-valued functions. | |
| Nov 12, 2011 at 6:41 | comment | added | Theo Johnson-Freyd | @Rasmus: hrm, it's now been a while since c-star-algebra class, and it's not my area. But my understanding is the following. First, when I say "algebra of functions", I never mean the algebra of bounded functions. In the real world, I usually want "all" functions, but when I am working c-star-algebraically, I mean "function that's less than $\epsilon$ outside a compact". Given $X$, the algebra of bounded functions is the algebra of functions on the Stone-Cech completion $\beta X$ of $X$, and it's not surprising for $\beta X$ to have better properties than $X$. | |
| Nov 11, 2011 at 21:52 | comment | added | Rasmus | Concerning "...a space is locally compact Hausdorff iff its algebra of continuous functions is commutative c-star algebra": Unless I misunderstand the statement, it is not true: For any topological space $X$, the bounded functions $X\to \mathbb C$ form a commutative $C^*$-algebra. | |
| Nov 20, 2009 at 23:54 | vote | accept | Julio César Salazar García | ||
| Nov 20, 2009 at 4:10 | history | answered | Theo Johnson-Freyd | CC BY-SA 2.5 |