Timeline for Which elements live in the image of the canonical map $X \otimes_\mathcal{F} M \to B(M_*, X)$?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 8, 2022 at 16:35 | vote | accept | J. De Ro | ||
| Sep 8, 2022 at 6:43 | comment | added | Matthew Daws | I deleted some comments which no longer make sense given the edits to the question. In recompense, I have added an answer. | |
| Sep 8, 2022 at 6:42 | answer | added | Matthew Daws | timeline score: 2 | |
| Sep 8, 2022 at 5:58 | history | edited | J. De Ro | CC BY-SA 4.0 |
deleted 222 characters in body
|
| Sep 8, 2022 at 5:57 | comment | added | J. De Ro | @YemonChoi I'm only assuming X to be norm-closed, but if you know a solution when X is sigma weakly closed that's also welcome! | |
| Sep 7, 2022 at 23:17 | comment | added | Yemon Choi | In your definition of the Fubini tensor product you are only considering slices by $\sigma$-weakly continuous functionals. Does this mean you are assuming $X$ to be $\sigma$-weakly closed? | |
| Sep 7, 2022 at 23:13 | comment | added | Yemon Choi | I'm not sure what is meant in the last paragraph although I agree that finding a properly self-contained account is not so easy (at least I never quite succeeded). If X and M are vN algebras then their Fubini tensor product equals their normal spatial tensor product by Tomita's commutant theorem, and this in turn equals $CB(M_*,X)$ by a result of Effros and Ruan (Int JMath 1990 Theorem 3.2). | |
| Sep 7, 2022 at 16:58 | history | asked | J. De Ro | CC BY-SA 4.0 |