Timeline for Standard form of fiber product of von Neumann algebras
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Sep 25 at 8:58 | comment | added | André Henriques | @DavidGao Yes. The image of $1\in L^2(A,\phi)$ under the isomorphism $L^2(A,\phi)\cong L^2(A)$ is thing which I denoted by $\sqrt\phi\in L^2(A)$. | |
| Sep 24 at 16:51 | comment | added | David Gao | In the $\sigma$-finite case, $L^2(A)$ can be identified with $L^2(A, \varphi)$ for some faithful $\varphi$ and similarly for $L^2(B)$. Then $1 \otimes 1 \in L^2(A) \boxtimes_Z L^2(B)$ induces a faithful state $\psi$ on $A \times_Z B$. Then $ab \in L^2(A \times_Z B) \to a \otimes b \in L^2(A) \boxtimes_Z L^2(B)$ should be an isomorphism. | |
| Sep 24 at 15:32 | history | edited | André Henriques | CC BY-SA 4.0 |
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| Sep 24 at 9:56 | history | asked | André Henriques | CC BY-SA 4.0 |