Timeline for Closability of a natural bimodule map between cyclic correspondences of von Neumann algebras
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 30, 2021 at 11:16 | vote | accept | Jon Bannon | ||
| Jul 30, 2021 at 11:01 | answer | added | Matthew Daws | timeline score: 1 | |
| Jul 29, 2021 at 2:13 | comment | added | Narutaka OZAWA | Well, I guess so, even though I'm not 100% sure because I'm not that knowledgeable of type III von Neumann algebras. | |
| Jul 29, 2021 at 1:35 | comment | added | Jon Bannon | @NarutakaOZAWA: Thank you for the response. I think I have to go and look up what a measurable operator is in the type III case, since I'm only familiar with $\tau$-measurable operators with $\tau$ a semifinite trace. I gather that if a vector in $K$ does not correspond to a measurable operator, this implies that the associated operator is not closable? | |
| Jul 28, 2021 at 23:11 | comment | added | Narutaka OZAWA | No in general. First, if there is a closable $M$-$N$ bimodule map $T$ with $T\xi = \eta$, then $\eta$ belongs to the closed subspace $K$ spanned by $(M\vee N^{\mathrm{op}})' \xi$. When $(M\vee N^{\mathrm{op}})'$ has a type III summand, not all vectors in $K$ correspond to measurable operators. | |
| Jul 28, 2021 at 12:04 | history | asked | Jon Bannon | CC BY-SA 4.0 |