Timeline for Separable von Neumann algebra
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 16, 2016 at 9:28 | history | edited | Tomasz Kania | CC BY-SA 3.0 |
added 16 characters in body
|
| Mar 16, 2016 at 1:46 | comment | added | Nik Weaver | @YemonChoi: maybe just how "immediate" depends on how you define von Neumann algebras, but it should be pretty easy regardless. If you take "von Neumann algebra" to be a WOT-closed unital *-subalgebra of $B(H)$ I think it's pretty immediate ... | |
| Mar 16, 2016 at 0:45 | comment | added | Yemon Choi | @NikWeaver I guess the "immediately" implicitly contains some argument about a vN alg being monotone complete? | |
| Mar 15, 2016 at 23:03 | comment | added | Nik Weaver | But proving this fact --- that every infinite dimensional C*-algebra contains an infinite dimensional abelian subalgebra --- is no easier than directly proving that every infinite dimensional von Neumann algebra contains infinitely many pairwise orthogonal projections, which immediately entails that it contains a copy of $l^\infty$. (This is the method used in Francesco's reference.) | |
| Mar 15, 2016 at 20:32 | history | answered | Tomasz Kania | CC BY-SA 3.0 |