Hi, It is known that the double commutant of the CCR algebra in it's GNS space with respect to some quasi-free states are always type III factors. My question is; Will some of them be hyperfinite factors?
Yes, Araki-Woods showed they're always ITPFI factors and ITPFI factors are hyperfinite. See the following:
It's a bit of a monster paper, the stuff on CCR algebras is near the end.