# Hyperfiniteness of CCR algebra

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?

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Sorry for confusing Ccr with ccr;-) – Marc Palm Mar 21 '13 at 16:18
Just to pick up on Marc's comment: by CCR you mean canonical commutation relations, not completely continuous representations (aka liminal), right? – Yemon Choi Mar 21 '13 at 18:25
I answered that the later are alway type 1, but the op referred to the former. – Marc Palm Mar 22 '13 at 14:23

Yes, Araki-Woods showed they're always ITPFI factors and ITPFI factors are hyperfinite. See the following:

Araki-Woods, A classification of factors

It's a bit of a monster paper, the stuff on CCR algebras is near the end.

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Thanks Ollie for the right reference. – Panchugopal Mar 23 '13 at 9:53