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I started a bare minimum at quantum probability (redirecting noncommutative probability space etc.)
Some entries have long been secretly referencing such an entry, and I have cross-linked accordingly, for instance from von Neumann algebra and quantum computing.
I had the feeling somewhere we already had a detailed account of probability theory dually in terms of von NNeumann algebras, but if we do I didn’t find it(?)
added the pointer to Segal 65 “Algebraic integration theory”
added also pointer to the recent textbook Landsman 17.
A neat quick introduction is Gleason 09. But at the moment the server with the pdf seems to be down. We should upload a copy to the nLab server. Does anyone have a local copy? (I didn’t save mine, it seems.)
The address is giving me the paper: http://www.math.uchicago.edu/~may/VIGRE/VIGRE2009/REUPapers/Gleason.pdf
Okay, that’s strange, I still get no response from this address.
Could you be so kind to upload a copy to the nLab? Or else to mail a copy to my private email address? Thanks!
Is that Ok, now?
Thanks!!
(I took the liberty of uploading it to the main web (here), instead of your personal web. That seems more robust against future changes, such as migrations.)
Can anyone upload to the main web?
Yes. Sorry, I thought this was clear.
Now I was about to point you to the HowTo, only to see that it didn’t have a section on file upload. Now I have added one:
Ok, let’s hope the spammers don’t think to upload their nonsense.
@ Urs #1
I had the feeling somewhere we already had a detailed account of probability theory dually in terms of von NNeumann algebras, but if we do I didn’t find it(?)
You may be thinking of Bayesian interpretation of quantum mechanics (now linked from this article) and its spin-off JBW-algebraic quantum mechanics, both of which have been discussed here before. Or for specifically classical probability and commutative real von Neumann algebras (or equivalently associative JBW-algebras), see measurable locale. There's not a lot of detail there on this subject, but some of Dmitri's posts to MathOverflow cited in the References are relevant.
Thanks, good point to cross-link these entries.
Let me add that I'd love to see a succinct explanation of how to do classical probability theory using operators on von Neumann algebras, whether on the nLab or elsewhere, but I don't actually know one. Nor do I know enough to write one, although I'd like to learn enough.
I think that’s what the references Segal 65 and Whittle 92 are about.
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