Timeline for Measurable functions and unbounded operators in von Neumann algebras
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Nov 16, 2009 at 18:08 | comment | added | Dave Penneys | Yes. If you start with a von Neumann algebra $M$ acting on a Hilbert space $H$, then I think the above construction is what you want. If instead you start with an abstract von Neumann algebra (a $W^\ast$-algebra), then @Dmitri has provided many other constructions. You can always take $M$ acting on $L^2(M)$, but if you do this for $B(H)$ (using the trace as the normal, faithful, semi-finite weight), you won't get $H$. It depends what you're trying to do with it... | |
| Nov 16, 2009 at 7:22 | vote | accept | Semyon Dyatlov | ||
| Nov 16, 2009 at 7:22 | comment | added | Semyon Dyatlov | Thanks! I think I finally got it. Do you mean that you will first consider a "nice" action of $M$ on some Hilbert space (which always exists by some classical result) and then consider the unbounded operators on this new space that are affiliated with the old algebra? | |
| Nov 16, 2009 at 6:26 | history | answered | Dave Penneys | CC BY-SA 2.5 |