Timeline for Spectrum of $L^\infty(X,\mu)$
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 25, 2020 at 18:40 | answer | added | Terry Tao | timeline score: 14 | |
| Jun 8, 2012 at 19:27 | vote | accept | unknown is my last name | ||
| Jun 8, 2012 at 15:47 | comment | added | Matthew Daws | A related question on math.se: math.stackexchange.com/questions/81324/… | |
| Jun 8, 2012 at 11:58 | comment | added | Matthew Daws | @André: Okay, we agree to disagree I guess. +1 your answer. | |
| Jun 8, 2012 at 11:33 | comment | added | André Henriques | @Matthew: It's not a "standard fact"... it's a mathematical object. The OP is simply asking for extra information/intuition about that mathematical object. | |
| Jun 8, 2012 at 11:30 | answer | added | André Henriques | timeline score: 12 | |
| Jun 8, 2012 at 8:41 | comment | added | Matthew Daws | Unless I'm missing something, this is a very standard fact about abelian von Neumann algebras which can be found in standard texts, just as Amin and Yulia say. So voting to close, as not research level. | |
| Jun 8, 2012 at 8:31 | comment | added | Yulia Kuznetsova | Yes, a hyperstonean space will be the spectrum. For example, if $X=\mathbb Z$ with the counting measure, then the spectrum is $\beta Z$ (the Stone-Cech compactification). | |
| Jun 8, 2012 at 8:26 | comment | added | Amin | I've had a rough night, and might be missing something, but are you looking for the topological space which would be the Gelfand spectrum of the abelian $C*-$algebra $L^\infty$? If that's the case you should look for completely discontinuous spaces on Google, or have a look at Kadison-Ringrose, the part on VonNeumann algebras. | |
| Jun 8, 2012 at 7:56 | comment | added | Johannes Ebert | Why the vote to close? | |
| Jun 8, 2012 at 6:45 | comment | added | Yemon Choi | It doesn't directly affect your question, but I have a feeling that $L^\infty$ is only the dual of $L^1$ under certain mild conditions on your space and your sigma-algebra. | |
| Jun 8, 2012 at 5:43 | history | asked | unknown is my last name | CC BY-SA 3.0 |