Timeline for Definition of a von Neumann algebra
Current License: CC BY-SA 2.5
3 events
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| Feb 6, 2010 at 2:59 | comment | added | Dmitri Pavlov | Well, my guess is that one can denote by A* the linear span of positive normal functionals on A (here a positive normal functional is a positive functional that preserves all supremums that exist) and by A** the dual of A* as a Banach space. Then the canonical map A→A** is an isomorphism if and only if A is a von Neumann algebra (Sakai's theorem). However, it is unclear to me whether A* is the dual of A in some topology for all C*-algebras A (and not just von Neumann algebras). | |
| Feb 5, 2010 at 18:13 | comment | added | Yemon Choi | Trying to use normal functionals was my first guess, but as you say it's not clear how to get the notion to make sense for all $C^*$-algebras. Perhaps there is a decent notion of "order completion"? | |
| Feb 5, 2010 at 10:34 | history | answered | Matthew Daws | CC BY-SA 2.5 |