Timeline for Spectra of $C^*$ algebras
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 30, 2018 at 15:28 | history | edited | Todd Trimble | CC BY-SA 4.0 |
removed a link that is legally questionable (according to a prominent user)
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| Nov 15, 2009 at 17:32 | vote | accept | Gian Maria Dall'Ara | ||
| Nov 11, 2009 at 18:38 | comment | added | Harald Hanche-Olsen | Hmm. I'll add hyperstonean spaces to the list of things I want to learn more about some day. Thanks. | |
| Nov 11, 2009 at 17:27 | comment | added | Dmitri Pavlov | After all, the category of commutative von Neumann algebras is contravariantly equivalent to the category of hyperstonean spaces and hyperstonean maps between them, and this category is equivalent to the category of measurable spaces and measurable maps between them. Thus understanding hyperstonean spaces is the same thing as understanding measure theory. There is a complete classification of measurable spaces: Every measurable space is a coproduct of points and real lines. Thus the spectrum of $L^\infty(R)$ is the only non-trivial interesting example of a measurable space. | |
| Nov 11, 2009 at 17:23 | comment | added | Dmitri Pavlov | Well, you can say a lot about this space. Bounded functions on it are in bijective correspondence with equivalence classes of bounded functions on the original measurable space; clopen sets are in bijective correspondence with equivalence classes of measurable sets etc. etc. etc. From the viewpoint of topology this space is weird because it is extremally disconnected, therefore to understand what this space really is you need to use quite different methods from what you are used to. | |
| Nov 11, 2009 at 15:55 | comment | added | Harald Hanche-Olsen | Yes, but in a sense, this is just a way of getting out of difficulty by naming a hard-to-understand object, right? I am not saying this is useless or that one can't say a lot about this space, but it doesn't really give you a handle on what the spectrum is. (Though, as Bill Clinton famously said, it depends on what the meaning of the word “is” is.) | |
| Nov 11, 2009 at 15:23 | history | answered | Dmitri Pavlov | CC BY-SA 2.5 |