Some results on continuous deformed free group factors

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We construct a Fock space associated to a symmetric function Q:U× U → (-1,1), where U is a nonempty open subset of Rʲ for some j. Namely, we will have operator-valued distributions a(x) and a+(y) satisfying a(x)a+(y)-Q(x,y)a+(y)a(x)=δ(x-y). Analogous to the qij-Fock space of Bozejko and Speicher, we have field operators arising as the sum of the creation and annihilation operators. These operators generate a von Neumann algebra analogous to the free group factors, and we will show that they are factors which do not have property Γ. It was pointed out to us by an anonymous referee that this is a special case of a theorem of Krolak.